Problems in the Theory of Automata and Artificial Intelligence

Glushkov, V. M.

doi:10.1080/01969727108545831

Cited by 7 publications

(13 citation statements)

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“…As was noted in [2], explorations into artificial intelligence have the same final fundamental objective, namely, the creation of a model of the human brain and disclosure of the mystery of thought. As for individual problems, they constitute a rather numerous set and vary from the creation of heuristic programs that play chess to the creation of physical models of neurons or from the construction of a general theory of self-organizing systems to the development of concrete algorithms and devices for recognition of visual or sound patterns.…”

Section: A Model Of the Brainmentioning

confidence: 94%

“…In [2], in the capacity of a model of a computer, a new concept of an infinite automaton is proposed, which is suitable for the refinement of many practical problems of synthesis and optimization of logical structures of computers and can be used in solving these problems by formal algebraic methods. In this model, the central processing unit of a computer is represented in the form of a composition of two automata, namely, a control automaton and an operational automaton.…”

Section: Automata Theory and Discrete Transformersmentioning

confidence: 99%

“…The following fundamental theorem on the regularization of arbitrary microprograms was also proved: the transformation realized by any microprogram can be represented by an expression in the microprogram algebra generated by the same elementary operators and conditions that are used in this microprogram. Since the constructions of the microprogram algebra are general and the design of logical units of computers is only one of its numerous application domains, this algebra was called the algebra of algorithms [2] or a system of algorithmic algebras (SAA) [17] later on.…”

Section: Algebra Of Algorithms and Systems Of Algorithmic Algebrasmentioning

confidence: 99%

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Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

Kapitonova

2005

Cybern Syst Anal

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51Ideas and means of artificial intelligence are considered that are developed in works of V. M. Glushkov and are used in brain modeling, computer-aided training, automata theory, and systems of algorithmic algebras.Keywords: model of the brain, algorithms and coding, experiments in training of machines, automata theory, discrete transformers, algebra of algorithms, system of algorithmic algebras.

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Section: A Model Of the Brainmentioning

confidence: 94%

Section: Automata Theory and Discrete Transformersmentioning

confidence: 99%

Section: Algebra Of Algorithms and Systems Of Algorithmic Algebrasmentioning

confidence: 99%

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Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

Kapitonova

2005

Cybern Syst Anal

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“…The SAD project is the continuation of a project initiated by academician V. Glushkov at the Institute for Cybernetics in Kiev more than 30 years ago [2]. Its original title was "Evidence Algorithm".…”

Section: Introductionmentioning

confidence: 99%

System for Automated Deduction (SAD): A Tool for Proof Verification

Verchinine

Lyaletski

Paskevich³

2007

Automated Deduction – CADE-21

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Abstract. In this paper, a proof assistant, called SAD, is presented. SAD deals with mathematical texts that are formalized in the ForTheL language (brief description of which is also given) and checks their correctness. We give a short description of SAD and a series of examples that show what can be done with it. Note that abstract notion of correctness on which the implementation is based, can be formalized with the help of a calculus (not presented here).

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“…The SAD project is the continuation of a project initiated by academician V. Glushkov at the Institute for Cybernetics in Kiev more than 30 years ago [2]. The title of the original project was "Evidence Algorithm" and its goal was to help a working mathematician to verify long and tiresome but routine reasonings.…”

Section: Introductionmentioning

confidence: 99%

On Correctness of Mathematical Texts from a Logical and Practical Point of View

Verchinine

Lyaletski

Paskevich

et al.

Lecture Notes in Computer Science

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Abstract.Formalizing mathematical argument is a fascinating activity in itself and (we hope!) also bears important practical applications. While traditional proof theory investigates deducibility of an individual statement from a collection of premises, a mathematical proof, with its structure and continuity, can hardly be presented as a single sequent or a set of logical formulas. What is called "mathematical text", as used in mathematical practice through the ages, seems to be more appropriate. However, no commonly adopted formal notion of mathematical text has emerged so far.In this paper, we propose a formalism which aims to reflect natural (human) style and structure of mathematical argument, yet to be appropriate for automated processing: principally, verification of its correctness (we consciously use the word rather than "soundness" or "validity").We consider mathematical texts that are formalized in the ForTheL language (brief description of which is also given) and we formulate a point of view on what a correct mathematical text might be. Logical notion of correctness is formalized with the help of a calculus. Practically, these ideas, methods and algorithms are implemented in a proof assistant called SAD. We give a short description of SAD and a series of examples showing what can be done with it.

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Problems in the Theory of Automata and Artificial Intelligence

Cited by 7 publications

References 0 publications

Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

Formation and Development of Ideas of Artificial Intelligence in V. M. Glushkov’s Works

System for Automated Deduction (SAD): A Tool for Proof Verification

On Correctness of Mathematical Texts from a Logical and Practical Point of View

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