Mathematical cybernetics. In economics and management
CYBERNETICS, a discipline devoted to the study of control and communication systems in animals, organizations and mechanisms. The term was first used in this sense in 1948 by Norbert Wiener. Scientific and technical dictionary
Mathematical modeling capabilities
Any modeling object is characterized by qualitative and quantitative characteristics. Mathematical modeling gives preference to identifying quantitative features and patterns of development of systems. This modeling largely abstracts from the specific content of the system, but necessarily takes it into account when trying to display the system through the apparatus of mathematics. The truth of mathematical modeling, like mathematics in general, is verified not by correlation with a specific empirical situation, but by the fact of deducibility from other propositions.
Mathematical modeling is a broad area of intellectual activity. This is a rather complex process of creating a mathematical description of the model. It includes several stages. N.P. Buslenko identifies three main stages: constructing a meaningful description, a formalized scheme and creating a mathematical model. In our opinion, mathematical modeling consists of four stages:
first - a meaningful description of an object or process, when the main components of the system and the laws of the system are identified. It includes numerical values of known characteristics and parameters of the system;
second - formulation of an applied problem or the task of formalizing a meaningful description of the system. An applied problem contains a statement of research ideas, main dependencies, as well as the formulation of a question, the solution of which is achieved through formalization of the system;
third - building a formalized diagram of an object or process, which involves choosing the main characteristics and parameters that will be used during formalization;
fourth - transformation of a formalized scheme into a mathematical model, when the creation or selection of appropriate mathematical functions is underway.
An extremely important role in the process of creating a mathematical model of a system is played by formalization, which is understood as a specific research technique, the purpose of which is to clarify knowledge by identifying its form (method of organization, structure as a connection between content components). The formalization procedure involves the introduction of symbols. As A.K. Sukhotin notes: “To formalize a certain content area means to build an artificial language in which concepts are replaced by symbols, and statements are replaced by combinations of symbols (formulas). A calculus is created when from some symbolic combinations, according to fixed rules, others can be obtained.” At the same time, thanks to formalization, information is revealed that is not captured at the levels of meaningful analysis. It is clear that formalization is difficult in relation to complex systems characterized by the richness and variety of connections.
After creating a mathematical model, its application begins to study some real process. In this case, the set of initial conditions and required quantities is first determined. Here, several ways of working with the model are possible: its analytical study through special transformations and problem solving; the use of numerical solution methods, for example, the method of statistical tests or the Monte Carlo method, methods of simulation of random processes, as well as through the use of computer technology for modeling.
When mathematically modeling complex systems, it is necessary to take into account the complexity of the system. As N.P. Buslenko rightly notes, a complex system is a multi-level structure of interacting elements combined into subsystems of various levels. A mathematical model of a complex system consists of mathematical models of elements and mathematical models of interaction of elements. The interaction of elements is usually considered as the result of the totality of the effects of each element on other elements. An impact represented by a set of its characteristics is called signal. Therefore, the interaction of elements of a complex system is studied within the framework of the signal exchange mechanism. Signals are transmitted through communication channels located between elements of a complex system. They have inputs and outputs
yes. When constructing a mathematical model of a system, its interaction with the external environment is taken into account. In this case, the external environment is usually represented in the form of a certain set of objects influencing the elements of the system under study. Significant difficulties arise in solving such problems as displaying qualitative transitions of elements and systems from one state to another, displaying transient processes.
According to N.P. Buslenko, the mechanism of signal exchange as a formalized scheme of interaction of elements of a complex system with each other or with objects of the external environment includes the following components:
the process of generating the output signal by the element that produces the signal;
determination of the transmission address for each characteristic of the output signal;
passage of signals through communication channels and arrangement of input signals for elements receiving signals;
the response of the element receiving the signal to the received input signal.
Thus, through successive stages of formalization, “cutting” the original problem into parts, the process of constructing a mathematical model is carried out.
Features of cybernetic modeling
The foundations of cybernetics were laid by the famous American philosopher and mathematician, professor at the Massachusetts Institute of Technology. Norbert Wiener (1894-1964) in the work "Cybernetics, or Control and Communication in the Animal and the Machine" (1948). The word "cybernetics" comes from the Greek word meaning "helmsman." The great merit of N. Wiener is that he established the common principles of management activities for fundamentally different objects of nature and society. Management comes down to the transfer, storage and processing of information, i.e. to various signals, messages, information. The main merit of N. Wiener is that he was the first to understand the fundamental importance of information in management processes. Nowadays, according to academician A. N. Kolmogorov, cybernetics studies systems of any nature that are capable of perceiving, storing and processing information and using it for control and regulation.
There is a certain dispersion in the definition of cybernetics as a science, in the identification of its object and subject. According to the position of Academician A.I. Berg, cybernetics is the science of managing complex dynamic systems. The basis of the categorical apparatus of cybernetics consists of such concepts as “model”, “system”, “control”, “information”. The ambiguity in the definitions of cybernetics is due to the fact that different authors place emphasis on one or another basic category. For example, an emphasis on the category “information” forces us to consider cybernetics as the science of the general laws of receiving, storing, transmitting and transforming information in complex controlled systems, and preference for the category “control” - as the science of modeling the control of various systems.
Such ambiguity is quite legitimate, because it is due to the multifunctionality of cybernetic science, its fulfillment of diverse roles in knowledge and practice. At the same time, focusing interests on one or another function forces us to see all of science in the light of this function. Such flexibility of cybernetic science speaks of its high cognitive potential.
Modern cybernetics is a heterogeneous science (Fig. 21). It combines a set of sciences that study management in systems of various natures from a formal perspective.
As noted, cybernetic modeling is based on a formal representation of systems and their components using the concepts of “input” and “output”, which characterize the connections of an element with the environment. Moreover, each element is characterized by a certain number of “inputs” and “outputs” (Fig. 22).
Rice. 22. Cybernetic representation of the element
In Fig. 22 X 1 , X 2 ,...X M schematically shown: the “inputs” of the element, Y 1 , Y 2 , ...,U N are the “outputs” of the element, and WITH 1 , C 2,..., C K - its states. Flows of matter, energy, and information influence the “inputs” of an element, shape its states and ensure functioning at the “outputs”. A quantitative measure of the interaction between “input” and “output” is intensity, which represents, respectively, the amount of matter, energy, and information per unit of time. Moreover, this interaction is continuous or discrete. Now you can build mathematical functions that describe the behavior of the element.
Cybernetics considers a system as a unity of control and controlled elements. Managed elements are called a managed object, and control elements are called a control system. The structure of the control system is built on a hierarchical principle. The control system and the controlled one (object) are interconnected by direct and feedback connections (Fig. 23), and in addition, by communication channels. The control system, through a direct communication channel, influences the controlled object, correcting the environmental influences on it. This leads to a change in the state of the control object and it changes its impact on the environment. Note that feedback can be external, as shown in Fig. 23, or internal, which ensures the internal functioning of the system and its interaction with the internal environment.
Cybernetic systems are a special type of system. As L.A. Petrushenko notes, the cybernetic system
the topic satisfies at least three requirements: “1) it must have a certain level of organization and a special structure; 2) therefore be able to perceive, store, process and use information, i.e. be an information system; 3) have control according to the feedback principle. A cybernetic system is a dynamic system that is a set of communication channels and objects and has a structure that allows it to extract (perceive) information from its interaction with the environment or another system and use this information for self-government according to the feedback principle."
A certain level of organization means:
integration of controlled and control subsystems in a cybernetic system;
hierarchy of the control subsystem and the fundamental complexity of the controlled subsystem;
the presence of deviations of the controlled system from the target or from equilibrium, which leads to a change in its entropy. This predetermines the need to develop managerial influence on it from the management system.
Information is the basis of the cybernetic system, which perceives, processes and transmits it. Information represents information, knowledge of the observer about the system, a reflection of its measure of diversity. It defines the connections between the elements of the system, its “input” and “output”. The informational nature of the cybernetic system is due to:
The need to obtain information about the impact of the environment on the managed system;
the importance of information about the behavior of the system;
the need for information about the structure of the system.
Various aspects of the nature of information have been studied N. Wiener, K. Shannon, W. R. Ashby, L. Brillouin, A. I. Berg, V. M. Glushkov, N. M. Amosov, A. N. Kolmogorov etc. The Philosophical Encyclopedic Dictionary gives the following interpretation of the term “information”: 1) message, information about the state of affairs, information about something transmitted by people; 2) reduced, removed uncertainty as a result of receiving a message; 3) a message inextricably linked with control, a signal in the unity of syntactic, semantic and pragmatic characteristics; 4) transmission, reflection of diversity in any objects and processes (inanimate and living nature).
The most important properties of information include:
adequacy, those. correspondence to real processes and objects;
relevance, those. compliance with the tasks for which it is intended;
right, those. compliance of the method of expressing information with its content;
accuracy, those. reflection of relevant phenomena with minimal distortion or minimal error;
relevance or timeliness, those. the possibility of its use when the need for it is especially great;
universality, those. independence from individual private changes;
degree of detail those. detail of information.
Any cybernetic system consists of elements that are connected by information flows. It contains information resources, receives, processes and transmits information. The system exists in a certain information environment and is subject to information noise. Its most important problems include: preventing distortion of information during transmission and reception (the problem of the children's game of "deaf telephone"); creating a language of information that would be understandable to all participants in management relations (communication problem); effective search, receipt and use of information in management (the problem of use). The complex of these problems acquires a certain uniqueness and diversity in
depending on the specifics of control systems. Thus, in the information systems of public authorities, as noted by N. R. Nizhnik and O. A. Mashkov, there is a need to resolve the following problems: creating a service of information resources of public authorities and public administration; creating a legal basis for its functioning; formation of infrastructure; creating an information monitoring system; creating an information service system.
Feedback is a type of connection of elements when the connection between the input of an element and the output of the same element is carried out either directly or through other elements of the system. Feedback can be internal or external (Fig. 24).
Feedback management is a complex process that includes:
constant monitoring of system functioning;
comparison of the current functioning of the system with the goals of the system;
developing an impact on the system to bring it into line with the goal;
introduction of influence into the system.
Feedback can be positive or negative. In this case, positive feedback enhances the effect of the input signal and has the same sign as it. Negative feedback weakens the input signal. Positive feedback worsens the stability of the system, since it takes it out of balance, and negative feedback helps restore equilibrium in the system.
An important role in cybernetic modeling is played by the concepts of “black”, “gray” and “white” boxes. A “black box” is understood as a cybernetic system (object, process, phenomenon), regarding the internal organization, structure and behavior of the elements of which the observer (researcher) has no information, but it is possible to influence the system through its inputs and record its reactions at the output. The observer, in the process of manipulating the input and recording the results at the output, draws up a test report, the analysis of which makes it possible to clarify the “black box”, i.e. get an idea of its structure and the laws of transformation of the “input” signal into the “output” signal. Such a clarified box is called a “gray box,” which, however, does not give a complete idea of its contents. If the observer fully understands the content of the system, its structure and the signal conversion mechanism, then it turns into a “white box”.
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1.8. Cybernetic aspects of computer science
1.8.1. Subject of cybernetics
The word "cybernetics" comes from the Greek word meaning in translation
"helmsman". Its modern significance is associated with the scientific field, the beginning of which
was founded by the book of the American scientist Norbert Wiener “Cybernetics, or
control and communication in animals and machines,” published in 1948. Soon the subject
not only biological and technical systems, but also systems
of any nature, capable of perceiving, storing and processing information
and use it for management and regulation. Published in 1947
The Encyclopedia of Cybernetics says that it is “...the science of general laws
receiving, storing, transmitting and converting information into complex
control systems. In this case, control systems here mean
not only technical, but also any biological, administrative and social
systems." Thus, cybernetics and computer science are most likely
unified science. Today, cybernetics is increasingly considered a part of computer science, its
“highest” section, to some extent similar in position to the “highest”
mathematics" in relation to all mathematics in general (about the same
position in relation to computer science is also the science of “artificial
intelligence"). Computer science as a whole is broader than cybernetics, since in computer science
There are aspects related to computer architecture and programming that
cannot be directly attributed to cybernetics.
Cybernetic branches of computer science are rich in approaches and
models in the study of various systems and are used as an apparatus
many branches of fundamental and applied mathematics.
A classic and to a certain extent independent branch of cybernetics
consider operations research. This term refers to the use
mathematical methods to justify decisions in various fields
purposeful human activity.
Let us explain what is meant by “decision”. Let some efforts be made
event (in the industrial, economic or social sphere),
aimed at achieving a specific goal - such an event is called
"operation". The person (or group of persons) responsible for carrying out this
event, you have the opportunity to choose how to organize it. For example: you can
select the types of products that will be produced; equipment that
this will apply; distribute available funds one way or another, etc.
An “operation” is a controlled event.
A decision is a choice from a range of options available to the decision maker.
Decisions can be successful and unsuccessful, reasonable and
unreasonable. Solutions are called optimal, for one reason or another
more preferable than others. The purpose of operations research is
mathematical (quantitative) justification of optimal solutions.
Operations Research includes the following sections:
1) mathematical programming (justification of plans, programs
economic activity); it includes relatively independent
sections: linear programming, nonlinear programming,
dynamic programming (in all these names the term
"programming" arose historically and has nothing to do with
computer programming);
2) queuing theory, based on the theory of random processes;
3) game theory, which allows one to justify decisions made under conditions
incomplete information.
Please note that these sections are not directly related to computers and technical
systems. Others, which developed rapidly in the 1970s and 1980s. section of cybernetics
there were automatic (automated) control systems. This section
has a closed, autonomous character, historically established
on one's own. It is closely related to the development of technical systems
automated regulation and management of technological and
production processes.
Another classic branch of cybernetics is recognition
images, which arose from the problem of modeling in technical perception systems
a person of signs, objects and speech, as well as the formation of concepts in a person
(training in the simplest, technical sense). This section is largely
arose from the technical needs of robotics. For example, it is required that
the robotic assembler recognized the required parts. When sorting automatically (or
Rejection) of parts requires recognition ability.
The pinnacle of cybernetics (and all computer science in general) is the section
dedicated to the problems of artificial intelligence. Most modern
control systems have the property of making decisions - the property
intellectuality, i.e. they model intellectual activity
person when making decisions.
1.8.2. Managed systems
Despite the variety of problems solved in cybernetics, the variety of models,
approaches and methods, cybernetics remains a unified science thanks to the use
general methodology based on systems theory and systems analysis.
A system is an extremely broad, initial, not strictly defined concept.
It is assumed that the system has a structure, i.e. consists of relatively
isolated parts (elements), which are, nevertheless, in a significant
relationships and interactions. The significance of the interaction is that
thanks to it, the elements of the system acquire together a certain new function,
a new property that is not possessed by any of the elements separately. In that
is the difference between a system and a network, which also consists of individual elements, but not
interconnected by significant relationships. Compare, for example,
an enterprise whose workshops form a system, since only all together
acquire the ability to produce final products (and none of them in
alone will not cope with this task), and a network of stores that can work
independently of each other.
Cybernetics, as a science of control, studies not all systems in general, but
only managed systems. But the area of interests and applications of cybernetics
extends to a wide variety of biological, economic,
social systems.
One of the characteristic features of the controlled system is the ability
transition to different states under the influence of control actions. Always
there is a certain set of system states from which a choice is made
optimal condition.
Abstracting from the specific features of individual cybernetic systems and
highlighting patterns common to a certain set of systems that describe
changing their state under various control actions, we come to
concept of an abstract cybernetic system. Its components are not
concrete objects, but abstract elements characterized
certain properties common to a wide class of objects.
Since cybernetic systems are understood as controlled systems, in
They must have a mechanism that performs control functions. More often
In total, this mechanism is implemented in the form of organs specially designed for
control (Fig. 1.38).
Rice. 1.38. Schematic representation of a cybernetic system in the form
a set of control and controlled parts
The arrows in the figure indicate the influences exchanged between the parts
systems. An arrow going from the control part of the system to the controlled part,
stands for control signals. The control part of the system that generates
control signals are called a control device. Manager
the device generates control signals based on state information
controlled system (shown in the figure with an arrow from the controlled part
system to its control part) in order to achieve the required state
disturbing influences. A set of rules according to which information
entering the control device is processed into control signals,
called a control algorithm.
Based on the introduced concepts, you can define the concept
"control". Control is an influence on an object, selected from a set
possible impacts based on the information available for this purpose, improving
operation or development of this facility.
Control systems solve four main types of control problems: 1)
regulation (stabilization); 2) program execution; 3) tracking; 4)
optimization.
The objectives of regulation are to maintain system parameters –
controlled quantities – near some constant set values (x),
despite the effect of disturbances M affecting the values of (x). Available here in
form of active protection against disturbances, which is fundamentally different from passive
protection method. Active protection involves the development in control systems
control actions that counteract disturbances. Yes, the task
maintaining the required system temperature can be solved using
controlled heating or cooling. Passive protection consists of
giving an object such properties that the dependence of the parameters we are interested in
from external disturbances was small. An example of passive protection is
thermal insulation to maintain a given system temperature,
anti-corrosion coatings for machine parts.
The program execution task arises in cases where the specified values
controlled quantities (x) change over time in a known way, for example in
production when performing work according to a predetermined schedule. IN
in biological systems, examples of program implementation are the development
organisms from eggs, seasonal migrations of birds, metamorphoses of insects.
The task of tracking is to maintain as close a match as possible to some
controlled parameter x0(t) to the current state of the system, changing
in an unforeseen way. The need for tracking arises, for example, when
managing the production of goods in conditions of changing demand.
Optimization problems - establishing the best mode in a certain sense
operation or state of a managed object - are quite common, for example
management of technological processes in order to minimize losses of raw materials, etc.
Systems in which it is not used to generate control actions
information about the values that the controlled quantities take in the process
control systems are called open-loop control systems. The structure is like this
system is shown in Fig. 1.39.
Rice. 1.39. Open-loop control system
The control algorithm is implemented by the control device CU, which
provides monitoring of the disturbance M and compensation for this disturbance, without
using the controlled variable X.
On the contrary, in closed control systems for the formation of managers
influences, information about the value of controlled quantities is used.
The structure of such a system is shown in Fig. 1.40. Communication between weekends
parameters X and input Y of the same element of the controlled system
called feedback.
Rice. 1.40. Closed-loop control system
Feedback is one of the most important concepts of cybernetics, helping
understand many phenomena that occur in controlled systems of various
nature. Feedback can be found by studying processes
occurring in living organisms, economic structures, systems
automatic regulation. Feedback that increases the influence of the input
influence on the controlled parameters of the system is called positive,
reducing the influence of the input influence – negative.
Positive feedback is used in many technical devices
to enhance, increase the values of input influences. Negative
feedback is used to restore balance disturbed by external
impact on the system.
1.8.3. Functions of man and machine in control systems
A well-studied area of application of cybernetic methods is
technological and production sphere, industrial management
enterprise.
Challenges that arise in managing a medium- and large-scale enterprise
are already quite complex, but can be solved using electronic
computers. Enterprise management systems or
territories (regions, cities) using computers for processing and storage
information are called automated control systems (ACS). By
By their nature, such systems are man-machine, i.e. along with
the use of powerful computers presupposes the presence of a person with his
intelligence.
In human-machine systems the following division of functions is assumed
machine and man: the machine stores and processes large amounts of
information, provides information support for decision making
by a person; a person makes management decisions.
More often in human-machine systems, computers perform routine,
uncreative, labor-intensive processing of information, freeing up a person’s time
for creative activities. However, the goal of developing computer
(information) control technology is full automation
activities that include partial or complete release of a person from
the need to make decisions. This is due not only to the desire to unload
human, but also with the fact that the development of technology and technology has led to situations where
a person due to his inherent physiological and psychological limitations
simply does not have time to make decisions in real time
process, which threatens with catastrophic consequences, for example: the need
activation of emergency protection of a nuclear reactor, reaction to events,
occurring during spacecraft launches, etc.
A system that replaces a person must have intelligence, to some extent
similar to human - artificial intelligence. Research
direction in the field of artificial intelligence systems also refers to
cybernetics, however, due to its importance for the prospects of all computer science in
In general, we will consider it in a separate paragraph.
Control questions
1. What is the subject of the science “Cybernetics”?
2. Describe the problems solved in the scientific section “operations research”.
3. What place does the theory of automatic control and
regulation?
4. What does the concept of “system” mean?
5. What is a “control system”?
6. Describe the tasks that arise in control systems.
7. What is “feedback”? Give examples of feedback from others
you managed systems.
8. What is an automated control system?
9. What is the place of man and computer in man-machine control systems?
During the development of the scientific and technological revolution, the physical, chemical
and the biological impact of humans on nature. The stronger the impact, the
the means of managing them must be more effective, and the primary task of our
time it becomes not only and not so much the choice of optimal (economically
beneficial) management modes, how much anticipation and prevention
ever-increasing danger of the occurrence of irreversible natural processes that threaten
human existence and life on Earth in general. Hardly ever before
humanity has set itself a more complex and more responsible task.
One can argue about exactly when irreversible changes in nature will occur and in what ways.
there will be their consequences, but there is no doubt that the period allotted by history for the solution
this complex problem is not that big.
In this light, works on systems theory or systemology acquire special significance.
(more often called the “systems approach”, which, in fact, arose in connection with
the need to solve problems of similar complexity). Those works are especially valuable
system orientation, which not only sets out the basic principles of the methodology
systems theory, and demonstrates the effectiveness of a systems approach to solving
quite complex and relevant cybernetic problems. This book is
work of just this type: systematic both in subject and in the spirit of presentation.
In the first part of the book, the author examines in detail the essence of the systems approach, but the second
applies it to the solution of the most general semiotic problems of cybernetics. Both
parts of the book are original and have independent meaning.
One of the distinctive aspects of the book is its attempt to present the essence of systemology with
a single point of view. To do this, the author deeply analyzes the concepts underlying
the presented concept of systemology, and shows that these concepts are related to the laws and
categories of materialist dialectics and that the systemic approach is only
bringing knowledge of basic laws to the level of specific practical applications
development of nature, and not a new worldview, as is often imagined by theorists
systems theory in the West.
The author does not try to formalize the presentation itself, which, of course, would be
premature, although very tempting, but the manner adopted in the book
the presentation can be considered the first step in this direction.
When presenting a systematic approach, the main attention in G. P. Melnikov’s work is given to
that which unites the system into a single whole. Many authors, when studying complex
systems tend to either divide them into simpler parts and consider the connections between
parts as an obstacle to such division, or, conversely, concentrate all
attention only to the connecting links, to the network of relationships (structure) between parts and
elements of the whole and declare the nature of the connected elements to be unimportant for
formation of integrity. In contrast to them, G.P. Melnikov also pays attention to
structure of the whole, and on those properties that arise in each element due to
the very fact of the existence of the system as a certain unity, and the properties of the whole,
arising from the unique properties of the elements, showing the mechanisms
mutual agreement of all these parameters of the system formed with mandatory
interaction with the external environment.
Each system, insofar as it exists, must acquire the properties necessary
to counteract external forces (impacts of other systems) that tend to
destroy this system. The longer the system exists and the stronger the impacts,
to which it is exposed, the more so in the system as a whole and in each of its elements
the properties of mutual consistency developed in the process should manifest themselves
adaptation. It is these properties that Hegel had in mind when he said that in a drop
the properties of the ocean are reflected.
Identifying these common properties and discovering their root cause (hidden in the complex
external influences), called by the author the determinant of the system, opens up wide
opportunities for studying those properties of complex systems that, in fact,
make them “complicated”.
This allows us to take a fresh look at the concept of a system and discover such connections between
its parts and such features of its elements, the existence of which is often difficult and
suspect It was on this path that G.P. Melnikov, as a result of studying the properties
overwhelming number of languages in the world, it was possible to discover very specific types
dependencies between the grammar of a language and its phonetics and create a new, systemic
typology of languages, comparing the structure of languages according to the characteristics of their determinants.
The approach developed by the author makes it possible to quite clearly define the difference
systematic approach from the structural one. It turned out that these differences are essentially contained
in one postulate: the ideas of structuralists are based on the thesis that
there is a completely amorphous material from which the system (instantly) forms
properties of a given system element in accordance only with its place in the structure.
According to systemological views, there is no absolutely amorphous material. Every
the material carries the properties of previous systems in which it was previously included and, moreover,
developed in the process of adaptation in these systems the ability to one degree or another
maintain their acquired properties. Therefore, when such material is used for
formation of a new system, then there is a long-term adaptation of the old and
the formation of new properties during adaptation, i.e. at every point in time in every
element of the system there are two types of properties: initial (material),
reflecting the background of the material, and imposed by the system (structural),
determined by the determinant of the system.
The issues raised by the author regarding the relations of structural (“logical”,
“syntactic”) and substantial (“material”, “systematic”) in
real natural and artificial systems not only represent
general philosophical interest, but are also very important in constructing
human-machine systems, which are the main tool for solving the most
complex modern problems of cybernetics.
To effectively use such systems, it is necessary first of all to separate
solution process into two parts: machine-specific, formal,
correlating with the structure of the object being studied or constructed, with logic
interaction of its parts, and substantive, semantic, requiring consideration not
reducible to the structure of the features of the substance of the object and therefore assigned to
person. At the same time, the main concern of a person is the most complete
using the capabilities of technology so that the remaining unformalized
Part of the task turned out to be feasible for a real team of specialists.
A person’s ability to informally identify the formalized part of a task, like others
human ability to operate with informal objects is one of the greatest
mysteries of nature. Therefore, any attempt to penetrate this secret or at least outline
approaches to it are of great importance.
From this point of view, the concepts presented in the book open up very tempting
prospects. Although the author tries not to emphasize the connection of the ideas he develops with
problems of artificial intelligence, but it is quite definitely felt when
reading a book. At the same time, the author focuses on the central problem: how
does a person think, what role does language play in the thinking process, how does thought take on
words in the acts of communication of one person with another, and not on fashionable problems of creation
heuristic (humanoid) methods for solving artificial game problems. IN
In this regard, the book's problems concern the development of principles for constructing
integral robots (not heuristic programming).
The author comes to identifying these principles not so much from direct technical
experimentation, how much from the systemic interpretation of the rich semiotic,
linguistic and psychological material accumulated to date. IN
In connection with this, the book pays much attention to the analysis of such cardinal issues
cybernetics, as the origins of the ability to form recognition mechanisms,
forecasting, sign communication and modeling and assessment of possibilities
using these mechanisms for meaningful human-machine communication and
cars between each other. To economically describe typical components of these processes
the author introduces a specialized symbolic apparatus.
The presentation of the content proposed in the book is fundamental and
persuasiveness. However, it must be remembered that the issues discussed in the book relate to
present time is one of the most difficult to explain and understand, and therefore
The reader who takes up this book must prepare himself in advance for hard work. Many
I'll have to re-read the passages and think about a lot, but I can be sure
to say that the reader’s diligence as he delves deeper into the material of the book will be rewarded.
Rarely found in modern scientific literature, the content-evolutionary, and
non-formal logical type of deduction and the resulting ability to capture
patterns where previously only a random accumulation of facts was seen - here
This is by no means a complete list of what a sufficiently diligent and
attentive reader.
Let us now dwell in more detail on some of the particular issues raised in the book, and
on evaluating methods and results of their solution.
1. As is clear from the above, methodological aspects are not an end in themselves for the author; he
forced to pay serious attention to this aspect of the matter precisely because there is enough
He sets himself serious tasks in general cybernetics. But exactly
therefore, the first part of the work, devoted to the presentation of the author’s concept of systemic
approach is indeed a presentation of a fairly holistic concept.
The reader interested primarily in problems of systemology can
focus your attention on the first part of the book, considering its second part as
application demonstrating the fact that the concept presented can serve
an effective tool for solving the most complex problems of cybernetics.
The reader who is interested in the issues presented in the second part of the book can
consider its first part also as an appendix, but absolutely mandatory, otherwise
neither the premises nor the main pathos of the research conclusions will be understood by him.
2. The concept of a systems approach set forth by the author of the book, as already noted, has
first of all, not formally axiomatic, but clearly ontological, bodily
orientation, focused on such a formulation of basic concepts and
patterns of a systematic approach, which would allow for the clearest possible
engineering, biological and mental interpretation and, therefore, could be
a means not only of describing and understanding the nature of actually existing systems, but
and their design, their implementation on computers. In this regard, the book
not just “systemic”, but also actually “cybernetic”.
It is important to note that the dialectical nature of the basic laws of systemology,
presented in the author's concept is not simply declared, but demonstrated.
Based on the principles of dialectical development, the author reveals the nature
meaningful communication between a person and a machine, the same principles are used in
the methodological part of the work when introducing the initial concepts of the systems approach.
These concepts are not simply taken as indefinable, as is customary in
construction of axiomatic theories, but develop and deepen as they
use by retrospection through concepts derived from the first. This
creative cuisine, usually shyly hidden in publications, looks very
natural in the reasoning of the author, who stands on the position of dialectics. It gives him
opportunity to gain support in discussing the question of what the limits of acceptable
formalization of a systematic approach and that in principle should be based on accounting
laws of development and laws of contradiction, through the implementation of which one can create
an automaton endowed with the ability to carry out at least elementary creative acts,
without which plans for meaningful communication between man and machine are doomed to failure.
3. It should be noted that if the reader does not share the original dialectical beliefs
author, then the conclusions derived from them may seem unconvincing. That
fact that to solve many modern cybernetic problems it is necessary that
no one doubts that an automaton could carry out creative acts. Less
it is obvious that for this purpose one should deal not so much with the development of purely formal
algorithms for the behavior of the machine, how many ways to solve the problem along the way
cybernization of the laws of dialectical contradiction.
However, let us recall in this regard that the well-known series of negative results,
related to the possibilities of meaningful axiomatic theories, suggests that
that it cannot be deduced from the postulates of such theories
meaningfully something greater than what was implied in the postulates. So
Thus, the creative act is fundamentally connected with the choice of the postulates themselves from
available knowledge. This choice is made within the framework of induction.
As L.V. Krushinsky, who studies intelligence, showed in his latest works
animals, the simplest creative act of an animal is this
the use of existing experience, which leads to the identification of a generalization of the type
postulating an elementary law of nature as a non-trivial hypothesis about
structure of the world, not contained explicitly in previous experience, but
allowing the animal to interact with the outside world more appropriately.
If the essence of the inductive creative act lies in this, and we, constructing
automatic machine, we wish his intellectual level to be at least equal to
intellectual level of the animal, then it is necessary to check whether it is possible to purely
formally, based on initial experimental information, postulate
hypothesis, i.e. put forward a postulate that reveals non-trivial information in the original
data. The positive or negative result of such a check has
fundamental importance for choosing ways to solve the problem of artificial
intelligence.
The author proceeds from the second, negative answer to this question; formally this is not
justifying. But, as it turned out very recently, these, based on purely
qualitative considerations, the author’s initial ideas are valid and to some extent
in a certain sense. K. F. Samokhvalov proved a theorem, the conclusions from which
give a direct answer to the question under discussion.
4. Thus, the fundamental need to go beyond formal logic
when developing the principles of inductive generalization. without which it is impossible
meaningful human-machine communication currently has a strict
justification. However, from this the author of the book does not at all draw a conclusion about the fundamental
the futility of using a formal apparatus in solving the most complex
cybernetic tasks. On the contrary, clearly contrasting corporeality,
the substantiality of technical and natural systems, the incorporeality of their structural
models, he clearly outlines the range of phenomena whose description and construction
can and should rely, first of all, on the strict formal apparatus of logic and
mathematics in the modern understanding of these terms. This circle is limited deeply
adapted systems.
Through this key idea for the presented concept of the essence of adaptability
the author shows that the very concept of formal has considerable reserves for expansion without
loss of rigor. In this regard, it is interesting to note modern attempts to enrich
initial concepts of the foundations of mathematics, development of richer and more unusual
traditional point of view of theories aimed at taking into account the ontology of the studied
entities.
5. Methodological justification and deep significance of these works for enrichment
arsenal of the very principles of constructing formal theories is clearly interpreted in
in terms of the relationship between the formalizable and the non-formalizable, considered in
systemological concept of the author of the book. It is very important that the author proves
physical realizability of what is not accessible to strict formalization, and thanks to
this is clearly opposed not only by the physical object to its structural model, but also
actual content in communication - any technical communicative
units, despite the fact that both are embodied in the substance of the model or in
brain neurons. This will make it possible to systematize the initial concepts of semiotics,
show the internal connection and fundamental opposition between a sign and its
meaning, between meaning and meaning, between mental and linguistic
processes between natural and artificial languages.
Particularly important is the author’s position that the deeper the adaptation, even
inanimate, physical object, the more natural it is inherent
predisposition to such interaction with the external environment, which may
be considered as, although primitive, an act of identification, an act of anticipatory
reflections. In this regard, one cannot help but recall the words of V.I. Lenin that even the dead
nature has a property close to sensation...
6. I would like to express regret that such an abundance of cardinal scientific
problems are discussed in the volume of a small book. This circumstance appears to be
deprived the author of the opportunity to use his characteristic manner of presenting his
thoughts for which he is known among listeners of his speeches at conferences and
congresses, seminars and lectures, where he illustrates each of his positions
visual drawings and examples from a wide variety of scientific fields and industries
technology, from social and everyday situations. In this regard, I would like to note that
a surprisingly wide range of phenomena, to the analysis of which he applies the principles of his
systemological concept and from the work on which he identifies the weak links of this
concept, continuously improving it. This can be judged at least by
publications of the author, only a small part of which is given in the bibliography.
The limited volume of the book makes it clear that the need to present
at least the most important aspects of the proposed concept of a systems approach and
demonstrate its performance forced the author to abandon a wide
review and analysis of other system concepts.
The term “cybernetics” was originally introduced into scientific circulation by Ampere, who in his
fundamental work “Essay on the Philosophy of Sciences” (1834-1843) defined cybernetics
as a science of government, which should provide citizens
various benefits. And in the modern understanding - as the science of general
patterns of control processes and information transfer in machines, living
.
organisms and society, was first proposed by Norbert Wiener in 1948
It includes the study of feedback, black boxes and derived concepts such as
as control and communication in living organisms, machines and organizations,
including self-organizations. It focuses on how something (digital,
mechanical or biological) processes information, reacts to it and
changes or can be changed in order to better fulfill the first two
tasks. Stafford Beer called it the science of effective organization, and Gordon
Passcraz expanded the definition to include flows of information “from any sources”,
starting with the stars and ending with the brain.
An example of cybernetic thinking. On the one hand, the company is considered
quality of the system in the surrounding environment. On the other hand, cybernetic
control can be represented as a system.
A more philosophical definition of cybernetics, proposed in 1956 by L.
Couffignal, one of the pioneers of cybernetics, describes cybernetics as
"the art of ensuring the effectiveness of action." The new definition was
proposed by Lewis Kaufman (English): "Cybernetics is the study of systems and
processes that interact with themselves and reproduce themselves.”
Cybernetic methods are used to study the case when the action of a system
in the environment causes some change in the environment, and this change
appears on the system through feedback, which causes changes in the way
system behavior. The study of these “feedback loops” is where the methods lie.
cybernetics.
Modern cybernetics originated as interdisciplinary research, combining
areas of control systems, electrical theory
circuits, mechanical engineering, mathematical modeling, mathematical
logic, evolutionary biology, neuroscience, anthropology. These studies appeared
in 1940, mainly in the works of scientists on the so-called. Macy conferences.
Other areas of research that influenced the development of cybernetics or were influenced by
its influence - control theory, game theory, theory
systems (mathematical equivalent of cybernetics), psychology (especially neuropsychologists
I, behaviorism, cognitive psychology) and philosophy.
Sphere of cybernetics[edit | edit wikitext]
The object of cybernetics is all controlled systems. Systems that cannot be
management, in principle, are not objects of study of cybernetics. Cybernetics
introduces concepts such as cybernetic approach, cybernetic system.
Cybernetic systems are considered abstractly, regardless of their
material nature. Examples of cybernetic systems - automatic regulators
in technology, computers, human brain, biological populations, human society.
Each such system is a set of interconnected objects
(system elements) capable of perceiving, remembering and processing
information and exchange it. Cybernetics develops general principles
creation of control systems and systems for automation of mental work. Basic
technical means for solving cybernetics problems - computers. Therefore, the emergence
cybernetics as an independent science (N. Wiener, 1948) is associated with the creation in the 40s.
XX century of these machines, and the development of cybernetics in theoretical and practical
aspects - with the progress of electronic computing technology.
Cybernetics is an interdisciplinary science. It arose at the intersection of mathematics,
logic, semiotics, physiology, biology, sociology. It is characterized by analysis and identification
general principles and approaches in the process of scientific knowledge. The most significant
The theories united by cybernetics are the following [source not specified 156 days]:
Signal transmission theory
Control Theory
Automata theory
Decision theory
Synergetics
Theory of algorithms
Pattern recognition
Optimal control theory
Learning Systems Theory
In addition to analysis tools, cybernetics uses powerful tools
for the synthesis of solutions provided by mathematical analysis tools, linear
algebra, geometry of convex sets, probability theory and mathematical
statistics, as well as more applied areas of mathematics, such
such as mathematical programming, econometrics, computer science and others
derivative disciplines.
The role of cybernetics is especially great in the psychology of work and its branches,
as engineering psychology and psychology of vocational education.
Cybernetics is the science of optimal control of complex dynamic systems,
studying the general principles of control and communication that underlie the work of most
systems of various nature - from homing missiles and
high-speed computers to complex living
of an organism. Control is the transfer of a controlled system from one state to another
through the targeted influence of the manager. Optimal control -
this is a transfer of the system to a new state with the fulfillment of some criterion
optimality, for example, minimizing the costs of time, labor, substances or
energy. A complex dynamic system is any real object, elements
which are studied to such a high degree of interconnection and mobility that change
one element leads to changes in others.
Directions[edit | edit wikitext]
Cybernetics is an earlier but still used general term for many
items. These subjects also extend into the field of many other sciences, but
combined in the study of systems management.
Pure cybernetics[edit | edit wikitext]
Pure cybernetics, or second-order cybernetics, studies control systems as
concept, trying to discover its basic principles.
ASIMO uses sensors and intelligent algorithms to avoid obstacles
and move up the stairs
Artificial Intelligence
Second order cybernetics
Computer vision
Control systems
Emergence
Learning organizations
New cybernetics
Interactions of Actors Theory
Communication Theory
In biology[edit | edit wikitext]
Cybernetics in biology - the study of cybernetic systems in biological
organisms, primarily focusing on how animals adapt to
their environment, and how information in the form of genes is passed on from generation to generation
generation. There is also a second direction - cyborgs.
Thermal image of a cold-blooded tarantula on a warm-blooded human hand
Bioengineering
Biological cybernetics
Bioinformatics
Bionics
Medical cybernetics
Neurocybernetics
Homeostasis
Synthetic biology
Systems biology
Theory of complex systems[edit | edit wikitext]
Complex systems theory analyzes the nature of complex systems and the reasons behind
based on their unusual properties.
A method for modeling a complex adaptive system
Complex adaptive system
Complex systems
Theory of complex systems
In computing[edit | edit wikitext]
In computing, cybernetics methods are used to control
devices and information analysis.
Robotics
Decision support system
Cellular automaton
Simulation
Computer vision
Artificial Intelligence
Object recognition
Control system
ACS
In engineering[edit | edit wikitext]
Cybernetics in engineering is used to analyze system failures, in
where small errors and shortcomings can lead to the failure of the entire system.
Artificial heart, an example of biomedical engineering.
Adaptive system
Ergonomics
Biomedical Engineering
Neurocomputing
Technical cybernetics
Systems engineering
In economics and management[edit | edit wikitext]
Cybernetic control
Economic cybernetics
Operations Research
In mathematics[edit | edit wikitext]
Dynamic system
Information theory
Systems theory
In psychology[edit | edit wikitext]
Psychological cybernetics
In sociology[edit | edit wikitext]
Memetics
Social cybernetics
History[edit | edit wikitext]
In Ancient Greece, the term “cybernetics”, which originally meant the art of helmsman,
began to be used figuratively to denote the art of statecraft
leader of the city. In this sense, he, in particular,
used by Plato in his Laws.
Word fr. "cybernétique" was used in almost its modern meaning in 1834
year by the French physicist and systematizer of sciences André Ampere (French AndréMarie
Ampère, 1775-1836), to designate the science of management in his classification system
human knowledge:
Andre Marie Ampere
"CYBERNETICS. Relations between people and people studied<…>previous
sciences are only a small part of the objects that the government should take care of; his
maintenance of public order, execution of
laws, fair distribution of taxes, selection of people whom it should
appoint to positions, and everything that contributes to the improvement of social conditions.
It must constantly choose between the various measures most suitable for
achieving the goal; and only through deep study and comparison of different elements,
provided to him for this choice by the knowledge of everything that has to do with the nation, it
able to govern in accordance with his character, customs, means
the existence of prosperity by organization and laws that can serve as general
rules of conduct and by which it is guided in each special case. So,
only after all the sciences dealing with these various objects should we put this one,
which we are talking about now and which I call cybernetics, from the word of others.
Greek
the art of navigation, was used by the Greeks themselves in incomparably more
the broad meaning of the art of management in general.”
; is a word adopted at the beginning in a narrow sense to mean
κυβερνητιχη
James Watt
The first artificial automatic regulating system, the water clock, was
invented by the ancient Greek mechanic Ctesibius. In his water clock, water flowed out of
source, such as a stabilizing tank, into the pool, then from the pool to
watch mechanisms. Ctesibius's device used a cone-shaped flow to control
water level in your tank and adjusting the water flow speed accordingly,
to maintain a constant water level in the tank, so that it is not
overflowing, neither drained. It was the first artificial truly automatic
self-regulating device that did not require any external
interference between feedback and control mechanisms. Although they
Naturally, they did not refer to this concept as the science of cybernetics (they considered it
field of engineering), Ctesibius and other ancient masters such as Heron
The Alexandrian or Chinese scientist Su Song is considered one of the first to study
cybernetic principles. Study of mechanisms in machines with corrective
feedback dates back to the end of the 18th century, when James's steam engine
Watt was equipped with a control device, a centrifugal reverse regulator
communication in order to control the speed of the motor. A. Wallace described feedback
as "necessary to the principle of evolution" in his famous 1858 work. In 1868
year, the great physicist J. Maxwell published a theoretical article on managers
devices, was one of the first to consider and improve the principles
self-regulating devices.Ya. Uexküll used a feedback mechanism in his
function cycle models (German: Funktionskreis) to explain behavior
animals.
XX century[edit | edit wikitext]
Modern cybernetics began in the 1940s as an interdisciplinary field
research combining control systems, electrical circuit theory,
mechanical engineering, logic modeling, evolutionary biology,
neurology. Electronic Control Systems Begin the Work of a Bell Engineer
Labs of Harold Black in 1927 on the use of negative feedback to
amplifier control. The ideas also relate to Ludwig's biological work
von Bertalanffy in general systems theory.
Early applications of negative feedback in electronic circuits included
control of artillery installations and radar antennas during the Second
world war. Jay Forrester, graduate student in the Servomechanism Laboratory
at MIT, working during World War II
war with Gordon S. Brown to improve electronic control systems
for the American Navy, later applied these ideas to public organizations,
such as corporations and cities as the original organizer of the School of Industrial
management of the Massachusetts Institute of Technology at the MIT Sloan School of
Management (English). Forrester is also known as the founder of system dynamics.
W. Deming, total quality management guru, in whose honor Japan was founded in 1950
established its main industrial award, in 1927 it was young
specialist at Bell Telephone Labs and may have been influenced by work at
field of network analysis). Deming made "understanding systems" one of the four
pillars of what he described as deep knowledge in his book The New Economy.
Book being reviewed:
New lines of development in physiology and their relationship
with cybernetics // Philosophical questions of the physiology of higher nervous activity and
Psychology, M., Publishing House of the USSR Academy of Sciences, 1963.
* * *
Page 499.
After the main speeches, a discussion of the reports was held.
“Discussion of reports. Yu.P. Frolov (Moscow)..."
* * *
Page 501.
“...At the same time, my comrades in the Pavlovian school forgot that these reverse or circular
connections have been open for quite some time. You can read about them
in the wonderful work of A.F. Samoilov about circular rhythms of excitation, starting with
elementary circular movement of the nervous process in a turtle heart specimen and
ending with the communication taking place between the speaker
and the audience. Inverse physiological and psychological connections are a prototype
feedbacks in cybernetic devices. Cybernetics
does not have even the remotest idea of the diversity and power of these connections, which
constitute the essence of our communication in the cultural and social environment...”
It’s still beautiful and most importantly correctly said:
“...Cybernetics does not have even the remotest idea of the diversity and power of these
connections that constitute the essence of our communication
in a cultural, social environment...”
Note that A.F. Samoilov died in 1930. This work was published in
1930.
Therefore, his work was many years ahead of the work of all his followers who became
attribute the discoveries to themselves, including P.K. Anokhin and N.A. Bernstein.
It is worth noting that in a living organism there cannot be feedback by definition,
since what is primary and what is secondary in a living organism is still unclear. If we consider
that reception is primary, then feedback is efferent signals, and if
If we assume that will power is primary, then the afferent signals are reverse.
A.F. himself Samoilov, being a physiologist, understood these processes more deeply and
therefore, he could not introduce the concept of feedback, as it was incorrect for a living organism.
In his concept of a “vicious circle of reflex activity” there is neither a beginning nor
end, and this is precisely what determines its physiology for the living organism as a whole.
Numerous works have appeared in related fields. In 1935 the Russian
physiologist P.K. Anokhin published a book in which the concept of inverse
connections (“reverse afferentation”). Research continued, especially in the area
mathematical modeling of regulatory processes, and two key articles were
published in 1943. These works were Behavior, Purpose and Teleology.
Norbert Wiener and J. Bigelow (English) and the work “The Logical Calculus of Ideas,
relating to nervous activity" by W. McCulloch and W. Pitts (English).
Cybernetics as a scientific discipline was based on the work of Wiener, McCulloch and
others such as W. R. Ashby and W. G. Walter.
Walter was one of the first to build autonomous robots to aid research
animal behavior. Along with the UK and the US, an important geographical
the location of early cybernetics was France.
In the spring of 1947, Wiener was invited to a congress on harmonic analysis,
held in Nancy, France. The event was organized by the group
mathematiciansNicolas Bourbaki, where the mathematician S. Mandelbroit played a major role.
Norbert Wiener
During this stay in France, Wiener received an offer to write an essay
on the topic of unifying this part of applied mathematics, which is found in the study
Brownian motion (the so-called Wiener process) and in the theory of telecommunications.
The following summer, already in the United States, he used the term "cybernetics"
as the title of a scientific theory. This name was intended to describe the study
“purposeful mechanisms” and was popularized in the book “Cybernetics, or
control and communication in animal and machine" (Hermann & Cie, Paris, 1948). IN
In Great Britain, the Ratio Club was formed around this in 1949.
In the early 1940s, John von Neumann, better known for his work in mathematics and
computer science, made a unique and unusual addition to the world of cybernetics:
the concept of a cellular automaton and a “universal constructor”
(self-reproducing cellular automaton). The result of these deceptively simple
thought experiments became the precise concept of self-reproduction, which
cybernetics accepted as a basic concept. The concept that the same properties
genetic reproduction applied to the social world, living cells and even
computer viruses, is further proof of the universality
cybernetic research.
Wiener popularized the social implications of cybernetics by drawing analogies between
automatic systems (such as a variable steam engine) and
human institutions in his bestseller “Cybernetics and Society” (The Human
Use of Human Beings: Cybernetics and Society HoughtonMifflin, 1950).
One of the main research centers in those days was the Biological Computer
laboratory at the University of Illinois, which for almost 20 years, starting
since 1958, headed by H. Förster.
Cybernetics in the USSR[edit | edit wikitext]
Main article: Cybernetics in the USSR
The development of cybernetics in the USSR began in the 1940s.
The 1954 edition of the Philosophical Dictionary included a description of cybernetics as
"reactionary pseudoscience"
In the 60s and 70s, cybernetics, both technical and economic, had already become
make a big bet.
Decline and rebirth[edit | edit wikitext]
Over the past 30 years, cybernetics has gone through ups and downs, becoming increasingly
more significant in the field of studying artificial intelligence and biological
machine interfaces (that is, cyborgs), but, having lost support, lost
guidelines for further development.
Francisco Varela
Stuart A. Umpleby
In the 1970s, new cybernetics appeared in various fields, but especially in biology.
Some biologists were influenced by cybernetic ideas (Maturana and Varela,
1980; Varela, 1979; (Atlan (English), 1979), "realized that cybernetic metaphors
programs on which molecular biology was based were
a concept of autonomy impossible for a living being. Therefore, this
thinkers had to invent a new cybernetics, more suitable for
organizations that humanity discovers in nature - organizations that are not
invented by himself." The possibility that this new cybernetics is applicable to
social forms of organizations has remained the subject of theoretical debate since the 1980s
years.
In the economy, within the framework of the Cybersyn project, they tried to introduce cybernetic
command economy in Chile in the early 1970s. The experiment was
stopped as a result of the 1973 coup, the equipment was destroyed.
In the 1980s, new cybernetics, unlike its predecessor, was interested in
“the interaction of autonomous political figures and subgroups, as well as practical and
reflexive consciousness of objects that create and reproduce structure
political community. The main view is the consideration of recursiveness, or
self-dependence of political speeches, both in relation to the expression of political
consciousness, and in the ways in which systems are created on the basis of themselves."
Dutch sociologists Geyer and Van der Zouwen (Dutch) in 1978 identified
a number of features of the emerging new cybernetics. "One of the features of the new
cybernetics is that it considers information as constructed and
restored by man interacting with the environment. This
provides the epistemological foundation of science when viewed from the perspective
observer. Another feature of the new cybernetics is its contribution to overcoming
problems of reduction (contradictions between macro and microanalysis). So this is
connects the individual with society." Geyer and van der Zouwen also noted that
“the transition from classical cybernetics to new cybernetics leads to a transition from
classic problems to new problems. These changes in thinking include,
among others, changes from an emphasis on the controlled system to the control and factor,
which guides management decisions. And a new emphasis on communication between
several systems that try to control each other."
Recent efforts in the study of cybernetics, control systems and behavior in environments
changes, as well as in related fields such as game theory (group analysis
interactions), feedback systems in evolution and research on metamaterials
(materials with properties of atoms and their components beyond Newtonian properties),
have led to a revival of interest in this increasingly relevant area.
Famous scientists[edit | edit wikitext]
Ampere, Andre Marie (1775-1836)
Vyshnegradsky, Ivan Alekseevich (1831-1895)
Norbert Wiener (1894-1964)
William Ashby (1903-1972)
Heinz von Foerster (1911-2002)
Claude Shannon (1916-2001)
Gregory Bateson (1904-1980)
Klaus, Georg (1912-1974)
Kitov, Anatoly Ivanovich (1920-2005)
Lyapunov Alexey Andreevich (1911-1973)
Glushkov Viktor Mikhailovich (1923-1982)
Beer Stafford (1926-2002)
Berg, Axel Ivanovich (1893-1979)
Kuzin, Lev Timofeevich (1928-1997)
Povarov, Gelliy Nikolaevich (1928-2004)
Pupkov, Konstantin Alexandrovich (born 1930)
Tikhonov, Andrey Nikolaevich (1906-1993)
1.9. Artificial Intelligence Basics
1.9.1. Directions of research and development in the field of artificial
intelligence
Scientific direction related to machine modeling of human
intellectual functions - artificial intelligence - emerged in the mid-1960s.
Its emergence is directly related to the general direction of scientific and
engineering thought, which led to the creation of a computer - a direction towards
automation of human intellectual activity, so that complex
intellectual tasks, considered the prerogative of man, were solved by technical
means.
Speaking about complex intellectual tasks, it should be understood that only 300–400 years
ago, multiplication of large numbers was classified as such; however, having learned in childhood
the rule of column multiplication, modern people use it without thinking, and
This task is hardly “intellectually challenging” today. Apparently in a circle
These should include those tasks for which there are no “automatic” rules,
those. there is no algorithm (even a very complex one), following which always leads to
success. If, in order to solve a problem that seems to us today to be related to
specified circle, in the future they will come up with a clear algorithm, it will cease to be “complicated
intellectual."
Despite its brevity, the history of research and development of artificial intelligence systems
intelligence can be divided into four periods:
1960s – early 1970s – research on “general intelligence”, attempts
model general intellectual processes characteristic of humans: free
dialogue, solving various problems, proving theorems, various games (such as
checkers, chess, etc.), writing poetry and music, etc.;
1970s – research and development of approaches to formal knowledge representation
and inferences, attempts to reduce intellectual activity to formal
transformations of characters, strings, etc.;
since the late 1970s – development of specialized ones for certain subject areas
areas of intelligent systems of practical practical importance
(expert systems);
1990s – frontal work on the creation of fifth-generation computers built on
principles other than conventional mainframe computers, and software for them.
Currently, “artificial intelligence” is a powerful branch of computer science, which has
both fundamental, purely scientific principles, and highly developed technical,
applied aspects related to the creation and operation of workable samples
intelligent systems. The significance of these works for the development of computer science is such that
The emergence of a new fifth generation computer depends on their success. This one
a qualitative leap in the capabilities of computers - their acquisition of full
intellectual capabilities - forms the basis for the development of computer technology in
perspective and is a sign of new generation computer technology.
Any problem for which the solution algorithm is not known can be classified as
artificial intelligence. Examples include playing chess, medical
diagnostics, translation of text into a foreign language - to solve these problems it is not
There are clear algorithms. Two more characteristic features of artificial problems
intelligence: predominant use of symbolic (rather than numerical) information
form and the presence of choice between many options under conditions of uncertainty.
Let us list some areas where artificial methods are used
intelligence.
1. Perception and recognition of images (a task mentioned earlier as one of
directions of cybernetics). Now this means not just technical systems,
perceiving visual and audio information, encoding and placing it in
memory, and problems of understanding and logical reasoning during processing
visual and speech information.
2. Mathematics and automatic proof of theorems.
3. Games. Like formal systems in mathematics, games characterized by finite
number of situations and clearly defined rules, from the very beginning of research on
artificial intelligence have gained attention as preferred objects
research, a testing ground for the application of new methods. Intelligent systems
the level of a person of average ability was quickly reached and surpassed, however
The level of the best specialists has not yet been reached. The difficulties that arose turned out to be
characteristic of many other situations, since in their “local” actions
a person uses the entire amount of knowledge that he has accumulated throughout his life.
4. Problem solving. In this case, the concept of “solution” is used in a broad sense,
refers to the formulation, analysis and presentation of specific situations, and
The tasks in question are those that occur in everyday life, for
solutions that require ingenuity and the ability to generalize.
5. Natural language understanding. Here the task is to analyze and generate texts, their
internal representation, identification of knowledge necessary for understanding texts.
The difficulties arise, in particular, from the fact that a significant part of the information in ordinary
dialogue is not expressed definitely and clearly. Natural language sentences have:
incompleteness;
inaccuracy;
vagueness;
grammatical incorrectness;
redundancy;
context dependent;
ambiguity.
However, such properties of the language, which is the result of centuries-old historical
development, serve as a condition for the functioning of language as a universal means
communication. At the same time, understanding natural language sentences by technical
systems are difficult to model due to these features of the language (and
the question of what “understanding” is needs clarification). In technical systems
formal language must be used, the meaning of the sentences is clear
determined by their shape. Translation from natural language to formal language is
non-trivial task.
6. Identification and presentation of specialist knowledge in expert systems. Expert
systems – intelligent systems that have absorbed the knowledge of specialists in
specific types of activities - are of great practical importance, with success
are used in many areas such as computer-aided design,
medical diagnostics, chemical analysis and synthesis, etc.
In all these areas, the main difficulties are related to the fact that they have not been sufficiently studied and
the principles of human intellectual activity, the process of making
solutions and problem solving. If in the 1960s. The question “can
computer to think”, now the question is posed differently: “is a person good enough
understands how he thinks in order to transfer this function to the computer"? Due to this,
work in the field of artificial intelligence is closely related to research on
relevant sections of psychology, physiology, linguistics.
1.9.2. Representation of knowledge in artificial intelligence systems
The main feature of intelligent systems is that they are based on
knowledge, or rather, on some representation of it. Knowledge here is understood as
stored (using a computer) information, formalized in accordance with certain
rules that a computer can use for logical inference according to certain
algorithms. The most fundamental and important problem is the description
semantic content of problems of the widest range, i.e. should be used
such a form of knowledge description that would guarantee its correct processing
content according to some formal rules. This problem is called problem
knowledge representations.
Currently, there are three best known approaches to representing knowledge in
systems discussed:
production and logical models;
Semantic networks;
frames.
Production rules are the simplest way to represent knowledge. It is based on
representation of knowledge in the form of rules structured according to a pattern
"IF - THEN." The “IF” part of the rule is called the premise, and the “THEN” part is called the conclusion or
action. The general rule is written as follows:
IF A1, A2, ..., An THEN B.
This notation means that “if all conditions from A1 to An are true, then B
is also true" or "when all conditions from A1 to An are satisfied, then
action B."
Consider the rule
IF
(1) y is the father of x
(2) z is the brother of y
THAT
z is x's uncle
In this case, the number of conditions is n = 2.
In the case n = 0, production describes knowledge consisting only of inference, i.e. fact.
An example of such knowledge is the fact “the atomic mass of iron is 55.847 amu.”
The variables x, y and z show that the rule contains some universal, general
knowledge abstracted from the specific values of variables. The same variable
used in output and various sendings, can receive various specific
meanings.
The knowledge presented in the intelligent system forms a knowledge base. IN
The intelligent system also includes an output mechanism that allows, based on
knowledge available in the knowledge base, obtain new knowledge.
Let us illustrate what has been said. Let us assume that in the knowledge base, together with the above
The rule also contains the following knowledge:
IF
(1) z is the father of x
(2) z is the father of y
(3) x and y are not the same person
x and y are brothers
THAT
Ivan is Sergei's father
Ivan is Pavel's father
Sergei is Nikolai's father
From the presented knowledge one can formally deduce the conclusion that Paul is
Uncle Nikolai. In this case, it is assumed that identical variables included in different
rules, independent; objects whose names these variables can receive are in no way
connected to each other. A formalized procedure using matching (with
which establishes whether two forms of representation coincide with each other, including
substitution of possible variable values), search in the knowledge base, return to the original
state when a solution attempt is unsuccessful, represents a mechanism of conclusions.
The simplicity and clarity of presenting knowledge with the help of products determined it
application in many systems, which are called production systems.
The semantic network is a different approach to knowledge representation, which is based on
depicting concepts (entities) using points (nodes) and relationships between them with
using arcs on a plane. Semantic networks are capable of representing the structure of knowledge
in all the complexity of their relationships, to link objects and their properties into a single whole. IN
As an example, a part of the semantic network related to
the concept of “fruit” (Fig. 1.41).
Rice. 1.41. Semantic Web Example
The frame system has all the properties inherent in the knowledge representation language, and
at the same time it represents a new way of processing information. The word "frame" in
translated from English means “frame”. The frame is the unit of presentation
knowledge about an object, which can be described by a certain set of concepts and
entities. The frame has a certain internal structure, consisting of a set
elements called slots. Each slot, in turn, is represented
a specific data structure, procedure, or may be associated with another frame.
Frame: human
Class
Animal
Structural element
Head, neck, arms, legs,...
Height
30–220 cm
Weight
1–200 kg
Tail
No
Analogy frame
Monkey
There are other, less common approaches to representing knowledge in
intelligent systems, including hybrid ones, based on the approaches already described.
Let us list the main features of machine data representation.
1. Internal interpretability. It is ensured that each information
units of its unique name, by which the system finds it to respond to
requests in which this name is mentioned.
2. Structure. Information units must have a flexible structure,
for them the “matryoshka principle” must be fulfilled, i.e. nesting of some
information units into others, it must be possible to establish
relationships such as “part – whole”, “genus – species”, “element – class” between individual
information units.
3. Connectivity. It must be possible to establish connections between different
type between information units that would characterize relationships
between information units. These relationships can be either declarative
(descriptive) and procedural (functional).
4. Semantic metrics. Allows you to establish situational proximity
information units, i.e. the magnitude of the associative connection between them. Such closeness
allows you to identify some typical situations in knowledge and build analogies.
5. Activity. The execution of actions in an intelligent system must be initiated
not by any external reasons, but by the current state of those represented in the system
knowledge. The emergence of new facts or descriptions of events, the establishment of connections should
become a source of system activity.
1.9.3. Modeling Reasoning
Reasoning is one of the most important types of human mental activity, in
the result of which he formulates on the basis of some sentences, statements,
judgments new sentences, statements, judgments. Valid mechanism
human reasoning remains insufficiently studied. Human
reasoning is characterized by: informality, vagueness, illogicality, broad
the use of images, emotions and feelings, which makes them extremely difficult
research and modeling. To date, the best studied logical
reasoning and many deductive inference mechanisms have been developed, implemented in
various intelligent systems based on knowledge representation using
1st order predicate logic.
A predicate is a construction of the form P(t1, t2, ..., tn), expressing some kind of connection between
some objects or properties of objects. The designation of this connection, or property,
P is called a "predicate symbol"; t1, t2, …, tn are called terms, they denote
objects connected by property (predicate) R.
Therms can only be of the following three types:
1) constant (denotes an individual object or concept);
2) variable (denotes different objects at different times);
3) compound term – function f(t1, t2, …, tm), having terms t1 as m arguments,
t2, ..., tm.
Example 1.
1. The sentence “The Volga flows into the Caspian Sea” can be written as a predicate
flows into (Volga, Caspian Sea).
“Falls in” is a predicate symbol; “Volga” and “Caspian Sea” are thermal constants. We
could indicate the relation “flows into” and the objects “Volga” and “Caspian Sea”
symbols.
Instead of thermal constants, we can consider variables:
flows into (X, Caspian Sea)
flows into (X, Y).
These are also predicates.
2. Ratio x + 1< у можно записать в виде предиката А(х, у). Предикатный символ А
here denotes what “remains” from x + 1< у, если выбросить из этой записи
variables x and y.
So, a predicate is a logical function that takes the values “true” or “false” in
depending on the values of its arguments. The number of arguments to a predicate is called
its arity.
So, for our examples, the predicate “falls” has arity 2 and when X = “Volga”, and Y =
“Caspian Sea” is true, but when X = “Don”, Y = “Bay of Biscay” is false. Predicate
And in example 2 it also has arity 2, is true when X = 1, Y = 3 and false when X = 3, Y = 1.
Predicates can be combined into formulas using logical connectives (conjunctions): ^
↔
(AND, conjunction), v (OR, disjunction), ~ (NOT, negation),
(“should”, implication),
(“if and only if”, equivalence).
→
The truth table (Table 1.15) of these conjunctions allows you to determine whether it is true or false
the meaning of the linking formula for different values of the predicates A and B included in it (and –
true, l - false).
Table 1.15
Truth of predicate connectives
A
IN
A^B
A v B
~A
A
A
B→
B↔
And
And
And
And
l
And
And
And
l
l
And
l
l
l
l
And
l
And
And
And
l
l
l
l
l
And
And
And
Mathematically strictly, the formulas of predicate logic are defined recursively:
1) a predicate is a formula;
2) if A and B are formulas, then A, B, A ^ B, A v B, A
3) there are no other formulas.
→
B, A
↔
B – also formulas;
Many predicate logic formulas require the use of quantifiers that define
the range of values of variables - arguments of predicates. Quantifiers are used
generalities: (inverted A from the English All - everything) and the quantifier of existence (inverted E
from English Exists – exists). The entry x reads “for any x”, “for every x”; X -
“x exists”, “for at least one x”. Quantifiers link predicate variables, to
which they operate and transform predicates into statements.
Example 2.
Let us introduce the following notation: A(x) – student x is an excellent student; B(x) – student x receives
increased stipend. Now formula A (Ivanov)
Ivanov is an excellent student, therefore, student Ivanov receives an increased scholarship,
and a formula with a general quantifier (x) (A(x)
He studies well and receives an increased scholarship.
B(x)) means: every student who
V (Ivanov) means: student
→
→
Of all the possible formulas, we need only one type of them, called phrases
Horna. Horn phrases generally contain implication and conjunction of predicates A,
B1, B2, ..., Bn as follows: B1, B2, ..., Bn
A, or in more convenient notation:
→
A: – B1, B2, ..., Bn
(reads: And if B1 and B2 and... and Bn).
Obviously, Horn's phrase is a form of writing a certain rule, and in what follows it will be
be called a rule. Predicate A is called the head or head of the rule, and
predicates B1, B2, ..., Bn are its subgoals.
Obviously, the individual predicate is a special case of Horn's phrase: A.
Another special case of Horn's phrase is the headless rule.
: – B1, B2, ..., Bn,
Horn's phrase is called a question. We will write ":-B" as "? – B”, and
“: – B1, B2, ..., Bn” in the form “? – B1, B2, ..., Bn.”
A) →
Let us explain the logical meaning of this formula. Recall that the implication A: – B (B
can be expressed through negation and disjunction: ~B v A (check this with
truth tables). This means that if we discard A, only ~B remains - the negation of B.
Formula
B1, B2, ..., Bn means the negation of the conjunction ~(B1 ^ B2 ^ ... ^ Bn), which according to
de Morgan's law ~(X ^ Y) = (~X) v (~Y) equals (~B1) v (~B2) v ... v (~Bn) – disjunctions
denials.
←
A set of Horn's phrases applied to some problem area forms a theory
(in a logical sense).
Example 3.
Let's consider a subject area: passing an exam in a certain discipline. Let's introduce
designations:
A – the student successfully passes the exam;
B – the student attended classes;
C – the student has mastered the educational material;
D – student studied independently;
E – the student prepared a cheat sheet.
Let us limit our knowledge about the subject area to the following statements:
the student will successfully pass the exam if the student has mastered the educational material;
the student has mastered the educational material if the student attended classes and the student studied
on one's own;
the student attended classes;
the student studied independently.
Logical notation form:
A: – C;
C: – B, D;
IN;
D.
In the example given, you can perform logical inference. So, from the truth of the facts
B and D and rules C: – B, D implies the truth of C, and from rule A: – C – truth
predicate A, i.e. the student will successfully pass the exam. In addition, rules A: – C and C: – B, D
could be rewritten as A: – B, D.
In these cases, inference rules called the resolution method are used.
Let's look at the simplest form of a resolution. Let's say there are “parent”
offers
negation: ~A
implication: A:– B.
As a result of one step of resolutive inference, we obtain a new sentence B, which
is called a resolvent. In this case, the resolution complies with the standard
propositional inference rule:
assuming that not A
and A if B
we output not V.
An even simpler case:
negation: ~A
fact: A.
The resolution is a contradiction.
In general, there are parent clauses
~(A1 ^ ... ^ Аn)
Аk:– В1, ..., Вm, 1 ≤ k< n.
As a resolvent, one output step yields ~(A1 ^ ... ^ Ak – 1 ^ B1 ^ ... ^ Bm ^
Аk + 1 ^ ... ^ Аn).
Thus, the resolution is a substitution of predicates - subgoals B1, ... Bm
instead of the corresponding predicate Ak from negation. Negation initiates logical
output and is therefore called a request (or question) and is denoted by A1, A2, ..., An.
The meaning of the resolution method is that the negation of the conjunction and
checks whether its value is true or false. If the value of the resulting
the conjunction is false, it means that the result is a contradiction and, since at the start there was
negation of predicates, proof “by converse” is performed. If received
value “true”, then the proof fails.
Example 4.
Let the predicate gives (X, Y, Z) mean that "X gives Y to some object Z" and
the predicate receive (X, Y) means "Y receives X". Let knowledge about these
relations are expressed by sentences:
1) receives (you, power): – gives (logic, power, you);
2) gives (logic, strength, you).
The problem to be solved is to answer the question: are you receiving
strength?
Let's imagine this question in the form of a negation ~receives (you, power). Resolution proposal
1 and negation leads to ~gives (logic, force, you), which together with fact 2 leads to
contradiction. Therefore, the answer to the original problem is “yes.”
So far we have looked at the resolution for statements or predicates without variables.
If the inference is made for a set of predicates with variables as
arguments, these variables receive the values of the corresponding
constants, or, as they also say, are specified by constants.
Let's explain this with an example.
Example 5.
Consider the following parent sentences:
1) ~gets (you, Y);
2) receives (X, strength): – gives (Z, strength, X).
They contain three variables X, Y and Z, which are implicitly affected by
general quantifier. Thus, sentence 1 states that "for all Y, you do not get Y"
and 2 – “for all Z, any X gains power if Z gives power to X.” Resolution rule
requires a match between the predicate from negation 1 and the head of rule 2. This means that
variables receive values (are instantiated) according to their place in
sentences 1 and 2 as follows: X = you, Y = power. Predicate receives (you, power)
is called a general example for the predicates gets(you, Y) and gets(X, power).
The stated provisions of predicate logic find implementation and further development in
Prolog programming language.
1.9.4. Pattern recognition
Pattern recognition is a set of methods and means of automatic
perception and analysis of the surrounding world.
The objectives of pattern recognition theory are:
automatic reading of typewritten or handwritten texts;
speech perception (regardless of the characteristics of the language and speaker);
Medical, psychological and pedagogical diagnostics;
automatic simultaneous translation from one language to another;
remote identification of objects, etc. There are two classes of images:
concrete and abstract.
Specific images are all real objects of the surrounding world, their images and
descriptions; abstract – concepts, categories, opinions, wishes, etc. In accordance with
This defines two recognition options: perceptual and conceptual.
In perceptual recognition systems (as a rule, these are technical systems)
the input element is a sensor whose task is to transform the physical
a quantity characterizing an observed object in the real world into another quantity,
intended for perception by its processing system. From a theoretical point of view
information sensor is an element for matching the input processing device
signals, and its output signals provide an “a priori” description of the observed object.
Sensor output signals are typically analogue-digital or
digital.
In conceptual systems, the role of a sensor is played by abstract, logical systems (such as
rules built on the principles of Boolean algebra).
Let's consider the main tasks and methods of pattern recognition.
Task 1. Studying the features of objects and clarifying the differences and similarities of the objects being studied
objects.
Example: periodic table of Mendeleev, classification of plants and animals
the world of Linnaeus and Darwin.
Task 2. Classification of recognized objects or phenomena. Main -
selection of a suitable classification principle.
Example: coin collector's collection, aircraft recognition.
Task 3. Compilation of a dictionary of features used for a priori description
classes, and for an a posteriori description of each unknown object. Signs
can be divided into logical (deterministic) and probabilistic.
Example: a machine designed to change coins. Coin recognition. Can
come up with different signs, but among them there are appropriate ones (diameter, mass).
Task 4. Description of object classes in the language of features.
Feature space method. Recognized objects have characteristics. Let G = (G1,
G2, ..., Gk ...) – a set of objects. Each object has characteristics C – (c1, c2, ...,
cn), among which there are essential and non-essential. Essential Features
we will call them defining and denote Y = (y1, y2, ..., ym). Let us define m-dimensional
space of object features, in which each point in space corresponds
object.
Example: consider a set of triangles as defining features
Let's take their sides, which we can measure (Fig. 1.42, a). It would be possible to take
corners, or one side and two corners, etc.
Rice. 1.42. Feature space method
The obtained data can be displayed in a three-dimensional feature space x1, x2, x3
(Fig. 1.42, b). Five classes (subspaces) can be distinguished in it: class
equilateral triangles x1 = x2 = x3, (a straight line representing the spatial
bisector); class of isosceles triangles x1 = x2 (plane passing through
axis x3 and bisector on the plane x1, x2); class of right triangles,
acute and obtuse triangles.
Thus, we identified classes (invented names and
class characteristics are defined). Further decision-making on object recognition
(an arbitrary triangle) is associated with determining the identity of the recognized
object to any class.
In general terms, the recognition problem can be formulated as a development problem
procedures for dividing a set of objects into classes.
Let G = (G1, G2, ..., Gk...) be a set of objects. For them n signs are defined,
which can be represented as a vector X = (x1, x2, ..., xn). Feature values
elements of a set of objects can be defined in three ways:
quantitatively (measurement of characteristic characteristics);
Probabilistic (the value is the probability of the event occurring);
alternatively (binary encoding – yes/no).
Let a set of objects be divided into m classes 1, 2, …, m. Required to highlight in
feature space of areas Di, i = 1, ..., m, equivalent to classes, i.e. if object
belongs to class k, then the corresponding point lies in the domain Dk.
Ω
Ω Ω
Ω
In an algebraic interpretation, the recognition problem can be formulated as follows
way.
It is required to construct separating functions Fi(x1, x2, ..., xn), i = 1, ..., m, having
properties: if some object with characteristics (x01, x02, ..., x0n)
i, then the value
Fi(x01, x02, ..., x0n) must be the largest. It should be the greatest for others too
values of attributes of objects related to
i, i.e.
Ω
Ω
Thus, the boundary of partitions, called the decisive boundary between the regions Di,
is expressed by the equation Fp(x) – Fg(x) = 0.
In Fig. Figure 1.43 shows the feature space model for the case of two-dimensional
spaces D1, D2 with corresponding classes 1, 2.
Ω Ω
Rice. 1.43. Illustration of the feature space method
The classification operation consists of distributing objects into classes, where under the class
is understood as a set of images that have the same characteristics. Same set
data can serve as a source of different classifications.
Example: finding a letter in the N letter alphabet is a task with N classes, find
vowels or consonants in the same alphabet is a task for two classes. Typically the number of classes
increases. If their number is unknown in advance, then they talk about learning “without a teacher”
(self-study). If the entire object space is divided, and sets of objects in classes
are not defined, then this is “supervised” learning.
Task 5. Development of a recognition algorithm that provides assignment
of a recognizable object to one or another class or some combination of them.
Example: recognition of an unknown word. Algorithms are based on comparison of one or
another measure of proximity or measure of similarity of the recognized object with any class.
Let us introduce the concept of distance between objects (the similarity of two objects). The less
the distance between two objects, the greater the similarity between them. Distance
between point P X and class X0 the quantity is called
d1(P, X0) = inf((P, M)|M X0).
The distance between two classes is determined by the value
d2(X1, X2) = inf(d1(P, M)|P X1, M X2).
In practice, the following distances are often used:
1. Euclidean distance
d2(Xi, Xj) = (∑|xik – xjk|2)1/2.
2. Distance in Manhattan (city block metric)
d2(Xi, Xj) = ∑|xik – xjk|.
3. Chebyshev distance
d3(Xi, Xj) = max |xik – xjk| (k).
Dictionary method. Let a catalog of all possible words classified by
length of words and arranged alphabetically. For example, consider service
Pascal programming language words:
etc., where N is the number of letters in the dictionary.
We define each character of the Latin alphabet by a sign, for example, its ordinal
number or frequency (probability) of its occurrence in the text.
Let us define the distance between a given letter and the letters of the alphabet as |xa – xb|, where xa –
a sign of a given letter, xb is a sign of a certain letter of the alphabet. Accept for
certainty as a sign of a letter its serial number in the alphabet:
A
IN
WITH
D
E
F
G
H
I
J
TO
L
M
N
ABOUT
R
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Let n = 4. Given a word with characteristics x1x2x3x4. For example, ELSE. In this case x1 = 5; x2 =
12; x3 = 19; x4 = 5. Let us denote (ai, xj) =
the letter located in the ith place in the alphabet, and the sign xj.
θ
ij = |аi – xj| – a number equal to the difference of the characteristic
θ
Let's find the distances in Manhattan for all the words from the dictionary
The smallest amount (distance) is associated with the second word of the dictionary. It defines
similarity to the recognized word.
Task 6. Image recognition.
Example: letter image recognition. The recognized image is obtained
in different ways and characterized by different quantities.
A raster object is more often represented as a given matrix relation of features.
For example, by overlaying an N x M grid on an image, you can determine in each cell
level of “blackness” or “grayness” (for black-and-white images) with numbers in the interval . In this case, 0 is white, 1 is black.
Thus, image A can be represented as a matrix
where the matrix elements further determine the degree of blackness of each i, jth cell.
Let a dictionary of images be known, for example, images of letters of the Russian alphabet.
In this case, we will assume that the corresponding blackness matrices represent
generalized letters, i.e. a composite image of letters of various fonts, typefaces and styles.
Let A1, A2, ..., Ap be a set of images (classes), H be a recognizable image.
Then the recognition task is reduced to searching for an instance (implementation) of Ak, the most
close in terms of distance to N.
Syntactic recognition. There is a separate class of problems related to
syntactic recognition of a given chain of some language in the sense of its
grammars. Grammar is the mechanism for creating language. There are generative and
recognizing grammars (Fig. 1.44).
Rice. 1.44. Generative and recognition grammars
A finite automaton recognizer is a set of five objects: A = (S, X, s0, d, F),
where S is a finite non-empty set (of states); X is a finite non-empty set
input signals (input alphabet); s0< S – начальное состояние; d: S x X
transition function; F – set of final states.
S – →
The finite automata recognizer A = (S, X, s0, d, F) admits an input chain of X*,
if this chain takes it from the initial state to one of the final ones
states.
The set of all chains allowed by an automaton A forms a language allowed by A.
A language for which there is a finite state machine that recognizes it is called
automatic language.
Examples of languages (V – alphabet, L – language):
1. V1 = (a, b, c); L= (abc, aa)
This is an incomplete automatic machine. (The final states are indicated by a double frame.)
2. V2 = (a, b, c); L = o.
Any automaton with an empty set of final states admits L.
3. V3 = (a, b, c); L = V*.
V* is a set of chains of arbitrary length.
An automaton with a single state that is final has three
transition from this state to the same
5. V5 = (0, 1); L = (set of even binary numbers)
6. V6 = (+, –, 0, ..., 9); L = (set of integer numeric constants)
7. V7 = (+, –, 0, ..., 9, "."); L = (set of real numbers)
Syntactic diagrams play a big role in computer science. Syntactic
diagrams are directed graphs with one input edge, one output edge
and labeled vertices. They define the language and are therefore generative
grammars of automata languages.
Valid chains: aab, aacabcb, etc.
Examples are syntax diagrams of the Pascal and C languages.
The following statement can be proven: any automaton language is given
syntax diagram and vice versa, using any syntax diagram you can
build a finite automaton (generally non-deterministic) that recognizes
the language in which the syntax diagram is specified.
By constructing the corresponding recognition automaton based on the syntactic diagram, we can
then implement this machine either in hardware or software. Thus,
syntactic diagrams serve not only for generation, but also for recognition
automata languages.
1.9.5. Intelligent information system interface
Analysis of the development of computer technology suggests that it
constantly evolving in two directions.
The first direction is related to improving the parameters of existing computers,
increasing their performance, increasing the volume of their operational and disk
memory, as well as with the improvement and modification of software,
aimed at increasing the efficiency of their functions.
The second direction determines changes in information processing technology,
leading to improved use of computer systems. Development in this
direction is associated with the emergence of new types of computers and qualitatively new
software tools that complement existing ones.
The development of software is moving along the path of increasing the user-friendliness of the interface,
those. such simplification of their management that the user does not require special
preparation and the system creates the most comfortable conditions for its work.
The main guideline in improving computing systems is turning them into
convenient partner for the end user when solving problems during his
professional activity.
To ensure the most user-friendly interface of the software with
The user must first become intelligent. Intelligent interface,
providing direct interaction between the end user and the computer
when solving a problem as part of a human-machine system, must perform three groups
functions:
providing the user with the opportunity to set a task for the computer by
messages only the conditions of the problem (without specifying a solution program);
providing the user with the opportunity to create problem solving environments with
using only terms and concepts from the field of professional activity
user, natural forms of information presentation;
ensuring flexible dialogue using a variety of means, including
regulated in advance, with correction of possible user errors.
Structure of the system (Fig. 1.45) that meets the requirements of the new solution technology
tasks consists of three components:
executive system, which is a set of means,
ensuring the implementation of programs;
A knowledge base containing a system of knowledge about the problem environment;
intelligent interface that allows for adaptation
computing system to the user and including a communication system and
problem solver.
This system differs significantly from those created at earlier stages.
development of informatics and computer technology. The path to implementing the latest
information technology involves the use of computer systems,
built on the basis of knowledge representation of the problem domain and
intelligent interface.
Rice. 1.45. Structure of a modern system for solving applied problems
1.9.6. Structure of a modern system for solving applied problems
The development of artificial intelligence systems first followed the path of modeling
general intellectual functions of individual consciousness. However, development
computer technology and software in the 1990s. refutes forecasts
previous decades about the imminent transition to fifth-generation computers.
Intellectual functions of the bulk of software communication systems on
natural language has not yet found wide application on an industrial scale.
Such a concept as “new information information” has undergone characteristic inflation.
technology". Initially, this concept meant an intelligent interface to the database
data, allowing application users to communicate with it directly on
natural language. Nowadays, “new information technologies” mean
simply technologies that use computer technology in information processing, in
including technologies based on the use of word processors and spreadsheets, and
also information systems.
Faced with insurmountable problems, the developers of a system with
"general" artificial intelligence, have taken the path of greater and greater
specialization, first towards expert systems, then towards individual
very specific intelligent functions built into instrumental
software tools that have not been considered until now the field of development for
artificial intelligence. For example, such systems now often have
capabilities of analytical mathematical calculations, translation of technical and
business texts, text recognition after scanning, parsing
phrases and sentences, self-adjustment, etc.
The research and development paradigm in artificial intelligence is gradually
is being revised. Apparently, the possibility of rapid development of software systems
modeling the intellectual functions of individual consciousness, largely
least exhausted. It is necessary to pay attention to new opportunities that
open information systems and networks in relation to public consciousness.
The development of computing systems and networks appears to lead to the creation of a new type
public consciousness, into which information media will be organically integrated
as a technological environment for processing and transmitting information. After this humanity
it will be hybrid human-machine intelligence that will receive not so much on a scale
individual consciousness as much as in the sphere of social practice.
Control questions
1. What is the history of the emergence and development of research on artificial
intelligence?
2. What are the distinctive features of problems in the field of artificial intelligence?
3. Describe the areas of research in artificial intelligence.
4. What is “knowledge” from the point of view of artificial intelligence systems?
5. What is the method of representing knowledge using products?
6. What is the basis of knowledge representation using the semantic network?
7. How can frame systems be used to represent knowledge?
8. What are the differences between knowledge representation in intelligent systems and representation
just data?
9. What does the concept of “predicate” mean?
10. What is a “Horn phrase”?
11. How does logical inference occur using the resolution method?
12. Check the validity of de Morgan’s laws: ~(X ^ Y) = (~X) v (~Y) and ~(X v Y) =
(~X) ^ (~Y).
13. In what direction are the interface parts of information systems developing?
14. What is the friendliness of the software interface?
15. What is the structure of promising information systems of the future?
CYBERNETICS, a management science that studies mainly by mathematical methods the general laws of receiving, storing, transmitting and converting information in complex control systems. There are other, slightly different definitions of cybernetics. Some are based on the informational aspect, others on the algorithmic aspect, and in others the concept of feedback is highlighted as expressing the specifics of cybernetics. In all definitions, however, the task of studying management systems and processes and information processes using mathematical methods is necessarily indicated. A complex control system in cybernetics is understood as any technical, biological, administrative, social, environmental or economic system. Cybernetics is based on the similarity of control and communication processes in machines, living organisms and their populations.
The main task of cybernetics is the study of general patterns underlying control processes in various environments, conditions, and areas. These are, first of all, the processes of transmission, storage and processing of information. At the same time, management processes take place in complex dynamic systems - objects with variability and the ability to develop.
Historical sketch. It is believed that the word “cybernetics” was first used by Plato in the dialogue “Laws” (4th century BC) to mean “government of people” [from the Greek ϰυβερνητιϰή - the art of governing, which is where the Latin words gubernare (to manage) and gubernator (governor) come from. ]. In 1834, A. Ampere, in his classification of sciences, used this term to refer to “the practice of government.” The term was introduced into modern science by N. Wiener (1947).
The cybernetic principle of automatic regulation based on feedback was implemented in automatic devices by Ctesibius (circa 2nd - 1st century BC; float water clocks) and Heron of Alexandria (circa 1st century AD). During the Middle Ages, many automatic and semi-automatic devices were created, used in clockwork and navigation mechanisms, as well as in water mills. Systematic work on the creation of teleological mechanisms, that is, machines that demonstrate appropriate behavior and are equipped with corrective feedback, began in the 18th century due to the need to regulate the operation of steam engines. In 1784, J. Watt patented a steam engine with an automatic regulator, which played a major role in the transition to industrial production. The beginning of the development of the theory of automatic regulation is considered to be J. C. Maxwell's article on regulators (1868). The founders of the theory of automatic control include I. A. Vyshnegradsky. In the 1930s, the works of I. P. Pavlov outlined a comparison of the brain and electrical switching circuits. P.K. Anokhin studied the activity of the body on the basis of the theory of functional systems he developed, and in 1935 he proposed the so-called method of reverse afferentation - a physiological analogue of feedback in controlling the behavior of the body. The final necessary prerequisites for the development of mathematical cybernetics were created in the 1930s by the work of A. N. Kolmogorov, V. A. Kotelnikov, E. L. Post, A. M. Turing, A. Church.
The need to create a science dedicated to describing control and communication in complex technical systems in terms of information processes and providing the possibility of their automation was realized by scientists and engineers during the 2nd World War. Complex systems of weapons and other technical means, command and control of troops and their supply in theaters of military operations have increased attention to the problems of automation of control and communications. The complexity and diversity of automated systems, the need to combine various control and communication means in them, and the new capabilities created by computers have led to the creation of a unified, general theory of control and communication, a general theory of information transmission and transformation. These tasks, to one degree or another, required a description of the processes being studied in terms of collecting, storing, processing, analyzing and evaluating information and obtaining a management or prognostic decision.
From the beginning of the war, N. Wiener (together with the American designer V. Bush) participated in the development of computing devices. Since 1943, he began developing computers together with J. von Neumann. In this regard, at the Princeton Institute for Advanced Study (USA) in 1943-44, meetings were held with the participation of representatives of various specialties - mathematicians, physicists, engineers, physiologists, neurologists. Here the Wiener-von Neumann group was finally formed, which included scientists W. McCulloch (USA) and A. Rosenbluth (Mexico); The work of this group made it possible to formulate and develop cybernetic ideas in relation to real technical and medical problems. The result of these studies was summed up by Wiener in his book Cybernetics, published in 1948.
Significant contributions to the development of cybernetics were made by N. M. Amosov, P. K. Anokhin, A. I. Berg, E. S. Bir, V. M. Glushkov, Yu. V. Gulyaev, S. V. Emelyanov, Yu. I. Zhuravlev, A. N. Kolmogorov, V. A. Kotelnikov, N. A. Kuznetsov, O. I. Larichev, O. B. Lupanov, A. A. Lyapunov, A. A. Markov, J. von Neumann , B. N. Petrov, E. L. Post, A. M. Turing, Ya. Z. Tsypkin, N. Chomsky, A. Church, K. Shannon, S. V. Yablonsky, as well as domestic scientists M. A Aizerman, V. M. Akhutin, B. V. Biryukov, A. I. Kitov, A. Ya. Lerner, Vyach. Vyach. Petrov, Ukrainian scientist A. G. Ivakhnenko.
The development of cybernetics was accompanied by its absorption of individual sciences, scientific directions and their sections and, in turn, the emergence in cybernetics and the subsequent separation of new sciences from it, many of which formed functional and applied sections of computer science (in particular, pattern recognition, image analysis, artificial intelligence). Cybernetics has a rather complex structure, and the scientific community has not reached complete agreement regarding the directions and sections that are its integral parts. The interpretation proposed in this article is based on the traditions of domestic schools of computer science, mathematics and cybernetics and on provisions that do not cause serious disagreements between leading scientists and specialists, most of whom agree that cybernetics is devoted to information, the practice of its processing and technology related to information systems; studies the structure, behavior and interaction of natural and artificial systems that store, process and transmit information; develops its own conceptual and theoretical foundations; has computational, cognitive, and social aspects, including the social implications of information technology as computers, individuals, and organizations process information.
Since the 1980s, there has been a slight decline in interest in cybernetics. It is associated with two main factors: 1) during the period of the formation of cybernetics, the creation of artificial intelligence seemed to many to be a simpler task than it actually was, and the prospect of its solution was in the foreseeable future; 2) on the basis of cybernetics, having inherited its basic methods, in particular mathematical ones, and almost completely absorbing cybernetics, a new science arose - computer science.
The most important research methods and connections with other sciences. Cybernetics is an interdisciplinary science. It arose at the intersection of mathematics, automatic control theory, logic, semiotics, physiology, biology and sociology. The formation of cybernetics was influenced by trends in the development of mathematics itself, the mathematization of various fields of science, the penetration of mathematical methods into many areas of practical activity, and the rapid progress of computer technology. The process of mathematization was accompanied by the emergence of a number of new mathematical disciplines, such as algorithm theory, information theory, operations research, game theory, which form an essential part of the apparatus of mathematical cybernetics. Based on problems in the theory of control systems, combinatorial analysis, graph theory, and coding theory, discrete mathematics arose, which is also one of the main mathematical tools of cybernetics. In the early 1970s, cybernetics was formed as a physical and mathematical science with its own subject of research - the so-called cybernetic systems. A cybernetic system consists of elements; in the simplest case, it can consist of one element. A cybernetic system receives an input signal (representing the input signals of its elements), has internal states (that is, sets of internal states of the elements are defined); By processing the input signal, the system transforms the internal state and produces an output signal. The structure of a cybernetic system is determined by many relationships connecting the input and output signals of the elements.
In cybernetics, the tasks of analysis and synthesis of cybernetic systems are of significant importance. The task of the analysis is to find the properties of information transformation carried out by the system. The task of synthesis is to construct a system according to the description of the transformation that it must carry out; in this case, the class of elements that the system can consist of is fixed. Of great importance is the problem of finding cybernetic systems that specify the same transformation, that is, the problem of the equivalence of cybernetic systems. If we specify the quality functional of cybernetic systems, then the problem arises of finding the best system in the class of equivalent cybernetic systems, that is, a system with the maximum value of the quality functional. Cybernetics also considers problems of reliability of cybernetic systems, the solution of which is aimed at increasing the reliability of the functioning of systems by improving their structure.
For fairly simple systems, the listed problems can usually be solved by classical means of mathematics. Difficulties arise in the analysis and synthesis of complex systems, which in cybernetics are understood as systems that do not have simple descriptions. These are usually cybernetic systems studied in biology. The direction of research, which has been given the name “theory of large (complex) systems,” has been developing in cybernetics since the 1950s. In addition to complex systems in nature, complex production automation systems, economic planning systems, administrative and economic systems, and military systems are studied. Methods for studying complex control systems form the basis of systems analysis and operations research.
To study complex systems in cybernetics, both an approach using mathematical methods and an experimental approach are used, using various experiments either with the object being studied or with its real physical model. The main methods of cybernetics include algorithmization, the use of feedback, the machine experiment method, the “black box” method, a systems approach, and formalization. One of the most important achievements of cybernetics is the development of a new approach - a method of mathematical modeling. It consists in the fact that experiments are carried out not with a real physical model, but with a computer implementation of a model of the object being studied, built according to its description. This computer model, including programs that implement changes in the parameters of an object in accordance with its description, is implemented on a computer, which makes it possible to conduct various experiments with the model, record its behavior under various conditions, change certain structures of the model, etc.
The theoretical basis of cybernetics is mathematical cybernetics, dedicated to methods for studying wide classes of cybernetic systems. Mathematical cybernetics uses a number of branches of mathematics, such as mathematical logic, discrete mathematics, probability theory, computational mathematics, information theory, coding theory, number theory, automata theory, complexity theory, as well as mathematical modeling and programming.
Depending on the field of application in cybernetics, they distinguish: technical cybernetics, including automation of technological processes, theory of automatic control systems, computer technology, theory of computers, automatic design systems, reliability theory; economic cybernetics; biological cybernetics, including bionics, mathematical and machine models of biosystems, neurocybernetics, bioengineering; medical cybernetics, which deals with the management process in medicine and healthcare, the development of simulation and mathematical models of diseases, the automation of diagnosis and treatment planning; psychological cybernetics, including the study and modeling of mental functions based on the study of human behavior; physiological cybernetics, including the study and modeling of the functions of cells, organs and systems under normal and pathological conditions for medical purposes; linguistic cybernetics, including the development of machine translation and communication with computers in natural language, as well as structural models of processing, analysis and evaluation of information. One of the most important achievements of cybernetics is the identification and formulation of the problem of modeling human thinking processes.
Lit.: Ashby W. R. Introduction to cybernetics. M., 1959; Anokhin P.K. Physiology and cybernetics // Philosophical issues of cybernetics. M., 1961; Logics. Automatic machines. Algorithms. M., 1963; Glushkov V. M. Introduction to cybernetics. K., 1964; aka. Cybernetics. Questions of theory and practice. M., 1986; Tsetlin M. L. Research on the theory of automata and modeling of biological systems. M., 1969; Biryukov B.V., Geller E.S. Cybernetics in the humanities. M., 1973; Biryukov B.V. Cybernetics and methodology of science. M., 1974; Wiener N. Cybernetics, or Control and Communication in Animals and Machines. 2nd ed. M., 1983; aka. Cybernetics and society. M., 2003; George F. Fundamentals of Cybernetics. M., 1984; Artificial Intelligence: Handbook. M., 1990. T. 1-3; Zhuravlev Yu. I. Selected scientific works. M., 1998; Luger J.F. Artificial intelligence: strategies and methods for solving complex problems. M., 2003; Samarsky A. A., Mikhailov A. P. Mathematical modeling. Ideas, methods, examples. 2nd ed. M., 2005; Larichev O.I. Theory and methods of decision making. 3rd ed. M., 2008.
Yu. I. Zhuravlev, I. B. Gurevich.
Missing No dataThe collection continues (since 1988) the mathematical focus of the world-famous series “Problems of Cybernetics”. The collection includes original and review articles on the main directions of world science, containing the latest results of fundamental research.
The authors of the collection are mainly well-known specialists; some of the articles were written by young scientists who have recently obtained striking new results. Among the areas presented in the collection are the theory of synthesis and complexity of control systems; problems of expressibility and completeness associated with multi-valued logics and automata in the theory of functional systems; fundamental issues of discrete optimization and recognition; problems of extremal problems for discrete functions (Feuer, Turan, Delsarte problems on a finite cyclic group); the study of mathematical models of information transmission in communication networks; a number of other branches of mathematical cybernetics are also presented.
Of particular note is the review article by O. B. Lupanov “A. N. Kolmogorov and the theory of circuit complexity.” Issue 16 – 2007. For specialists, graduate students, students interested in the current state of mathematical cybernetics and its applications.
Theory of information storage and retrieval
Valery Kudryavtsev Educational literature AbsentA new type of database representation is introduced, called an information graph data model, which generalizes previously known models. The main types of problems of searching for information in databases are considered and the problems of complexity of solving these problems in relation to the information graph model are investigated.
A mathematical apparatus for solving these problems has been developed, based on methods from the theory of complexity of control systems, probability theory, as well as on original methods of characteristic graph carriers, optimal decomposition and dimension reduction.
The book is intended for specialists in the field of discrete mathematics, mathematical cybernetics, recognition theory and algorithmic complexity.
Test recognition theory
Valery Kudryavtsev Educational literature AbsentA logical approach to pattern recognition is described. Its main concept is the test. Analysis of a set of tests allows us to construct functionals that characterize the image and procedures for calculating their values. Qualitative and metric properties of tests, functionals and recognition procedures are indicated.
The results of solving specific problems are presented. The book can be recommended to mathematicians, cybernetics, computer scientists and engineers as a scientific monograph and as a new technological apparatus, as well as a textbook for undergraduate and graduate students specializing in the field of mathematical cybernetics, discrete mathematics and mathematical computer science.
Problems in set theory, mathematical logic and theory of algorithms
Igor Lavrov Educational literature Missing No dataThe book systematically presents the foundations of set theory, mathematical logic, and the theory of algorithms in the form of problems. The book is intended for the active study of mathematical logic and related sciences. Consists of three parts: “Set Theory”, “Mathematical Logic” and “Theory of Algorithms”.
The problems are provided with instructions and answers. All necessary definitions are formulated in brief theoretical introductions to each paragraph. The 3rd edition of the book was published in 1995. The collection can be used as a textbook for mathematics departments of universities, pedagogical institutes, as well as in technical universities when studying cybernetics and computer science.
For mathematicians - algebraists, logicians and cybernetics.
Basics of the theory of Boolean functions
Sergey Marchenkov Technical literature Missing No dataThe book contains a detailed introduction to the theory of Boolean functions. The main properties of Boolean functions are outlined and the criterion of functional completeness is proved. A description of all closed classes of Boolean functions (Post classes) is given and a new proof of their finite generationability is given.
The definition of Post classes in terms of some standard predicates is considered. The foundations of Galois theory for Post classes are presented. Two “strong” closure operators are introduced and studied: parametric and positive. Partial Boolean functions are considered and a criterion of functional completeness for the class of partial Boolean functions is proved.
The complexity of implementing Boolean functions by circuits of functional elements is studied. For undergraduates, graduate students and higher education teachers studying and teaching discrete mathematics and mathematical cybernetics. The UMO on classical university education is approved as a teaching aid for students of higher educational institutions studying in the areas of higher education 010400 “Applied mathematics and computer science” and 010300 “Fundamental computer science and information technology”.
Numerical optimization methods 3rd ed., rev. and additional Textbook and workshop for academic bachelor's degree
Alexander Vasilievich Timokhov Educational literature Bachelor. Academic courseThe textbook is written on the basis of lecture courses on optimization, which over the course of a number of years were given by the authors at the Faculty of Computational Mathematics and Cybernetics of M.V. Lomonosov Moscow State University. The main attention is paid to methods for minimizing functions of a finite number of variables.
The publication includes theory and numerical methods for solving optimization problems, as well as examples of applied models that reduce to this type of mathematical problems. The appendix contains all the necessary information from mathematical analysis and linear algebra.
Physics. Practical course for university applicants
V. A. Makarov Educational literature AbsentThe manual is intended for graduating students of secondary schools with in-depth study of physics and mathematics. It is based on problems in physics that have been offered over the past 20 years to applicants to the Faculty of Computational Mathematics and Cybernetics of Moscow State University.
M. V. Lomonosov. The material is divided into topics in accordance with the program of entrance examinations in physics for applicants to Moscow State University. Each topic is preceded by a brief summary of basic theoretical information that is necessary to solve problems and will be useful in preparing for entrance exams.
In total, the collection includes about 600 problems, more than half of them are provided with detailed solutions and methodological instructions. For schoolchildren preparing to enter the physics and mathematics faculties of universities.
Optimization methods 3rd ed., rev. and additional Textbook and workshop for academic bachelor's degree
Vyacheslav Vasilievich Fedorov Educational literature Bachelor and Master. Academic courseThe textbook is written on the basis of lecture courses on optimization, which over the course of a number of years were given by the authors at the Faculty of Computational Mathematics and Cybernetics of Moscow State University. M. V. Lomonosov. The main attention is paid to methods for minimizing functions of a finite number of variables.
The publication includes problems. The appendix contains all the necessary information from mathematical analysis and linear algebra.
Intelligent systems. Theory of information storage and retrieval, 2nd ed., rev. and additional Tutorial for tank
The main types of problems of searching for information in databases are considered, and the problems of complexity of solving these problems in relation to the information graph model are explored.
Analytic geometry
V. A. Ilyin Educational literature Missing No dataThe textbook is written based on the teaching experience of the authors at Moscow State University. M. V. Lomonosov. The first edition was published in 1968, the second (1971) and third (1981) editions are stereotypical, the fourth edition (1988) was supplemented with material on linear and projective transformations.
Mathematical game theory is an integral part of a broad branch of mathematics - operations research. Game theory methods are widely used in ecology, psychology, cybernetics, biology - wherever many participants pursue different (often opposing) goals in joint activities.
But the main area of application of this discipline is economics and social sciences. The textbook includes topics that are basic and mandatory in the training of economists. It presents classic branches of game theory, such as matrix, bimatrix non-cooperative and statistical games, and modern developments, such as games with incomplete and imperfect information, cooperative and dynamic games.
The theoretical material in the book is widely illustrated with examples and provided with tasks for individual work, as well as tests.
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