Finite Automata

1st Edition

Behavior and Synthesis

Authors: A. de Vries
Hardcover ISBN: 9780720480214
eBook ISBN: 9781483297293
Imprint: Elsevier Science
Published Date: 1st January 1981
Page Count: 532
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This dictionary supplies associations which have been evoked by certain words, signs, etc. in Western civilization in the past, and which may float to the surface again tomorrow; for however 'daringly new' a modern use of imagery may look, it generally appears to have roots in what has been said and done in the past. No fine distinctions have been made between symbols (in the limited sense), allegories, metaphors, signs, types, images, etc. (not to mention 'ascending' and 'descending' symbols), since such subtle distinctions, however sensible from a scientific point of view, are useless to a person struggling with the deeper comprehension (and thus appreciation) of a particular 'symbol'.

Table of Contents


Chapter 0. Introduction

0.1. The Concept of an Automaton

0.2. Types of Automata

0.3. Automata and Graphs

0.4. Terminological Clarifications

0.5. Survey of the Contents of Chapters I to V


Chapter I. Behavior of Outputless Automata

I.1. Representation of Languages and ω-Languages in Automata

I.2. Interchangeability

I.3. Distinguishability of Words and ω-Words

I.4. Decidability of Properties of Finite Automata

I.5. Projections, Sources, Macrosources

I.6. Operations on Sources (Macrosources) and on the Languages (ω-Languages) Represented by them

I.7. Determinization of Sources. Operations Preserving Representability of Languages in Finite Automata

I.8. Determinization of Macrosources. Operations Preserving Representability of ω-Languages in Finite Automata

I.9. Proof of the Concatenation Theorem (Theorem 1.11)

I.10. Proof of the Strong Iteration Theorem (Theorem 1.12)

I.11. Probabilistic Automata

I.12. Grammars and Automata

Supplementary Material, Problems, Examples


Chapter II. Behavior of Automata with Output

II.1. Anticipation

II.2. Memory (Weight)

II.3. Equivalent Automata

II.4. Comparison of the Weight of an Operator with the Weight of an Automaton Realizing it

II.5. Representation of Languages (ω-Languages) and Realization of Operators. The Uniformization Problem

II.6. More About Decision Problems of Finite Automata

II.7. Games, Strategies and Nonanticipatory Operators

II.8. Game-Theoretic Interpretation of the Uniformization Problem

II.9. Proof of the Fundamental Theorem on Finite-State Games—Intuitive Outline


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© Elsevier Science 1973
Elsevier Science
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About the Author

A. de Vries