ALGEBRAIC THEORY OF AUTOMATA
F. GECSEG and I. PEAK

AKADEMIAI KIADO • BUDAPEST 1972.  str 329, stan bdb - (podniszczona lekko okładka)

ISBN

 
CONTENTS
Preface
Notations and general notions
CHAPTER   1
CONCEPT OF AUTOMATON
§ 1.1.   Types of automata
§1.2.   Presentation of automata  .
§ 1.3.    Subautomaton. Homomorphism and isomorphism
§ 1.4.    Extension of functions S and X
§ 1.5.    Quasi-automata and semiautomata
§ 1.6.   Free automata. Defining relations
§ 1.7.   Mappings induced by automata
§ 1.8.   A theorem on the application of automata for the study of non-automaton mappings
§ 1.9.   Reduced automata
§1.10. Equivalence of automata
§1.11. Minimization of automata
§1.12. Composition of automata
CHAPTER   2
ANALYSIS AND SYNTHESIS. ALGEBRA OF EVENTS
§ 2.1.    Concept of analysis and synthesis
§ 2.2.    Concept and algebra of events
§ 2.3.    Regular events
§ 2.4.    Representation of events by automata
§ 2.5.    Analysis of finite automata (in the general sense)
§ 2.6.   Synthesis of finite automata (in the general sense)
§ 2.7.    Connection between an automaton and the mapping induced by it, in the language of events
§ 2.8.    Mappings that can be induced by finite automata
§ 2.9.   Algebra of regular events. Transformations of events preserving regularity
§ 2.10. Equations and systems of equations in the algebra of events
§ 2.11. Systems of axioms in the algebra of regular events
§ 2.12. Event implications. Axiomatizable classes of automata
§ 2.13. Space of events.
CHAPTER   3
SOME SPECIAL CLASSES OF AUTOMATA
§3.1.    Commutative automata
§ 3.2.    Nilpotent automata
§ 3.3.    Definite, ultimate definite and symmetric definite automata
§ 3.4.    Linear automata
§ 3.5.    Pushdown automata
chapter  4
COMPOSITION OF AUTOMATA. AUTOMATON MAPPINGS
§ 4.1.    Complete systems of automata
§ 4.2.    Families of automaton mappings
§ 4.3.    i?-complete systems of automata
§ 4.4.    Semigroups of automaton mappings
§ 4.5.    Groups of automaton mappings
§ 4.6.    Representation of automaton mappings in bounded lengths
§ 4.7.    Metric groups of automaton mappings
CHAPTER   5
AUTOMATA AND SEMIGROUPS
§ 5.1.    Characteristic semigroups of automata
§ 5.2.    Endomorphism semigroups and automorphism groups of automata
§ 5.3.    Cyclic automata and quasi-automata
§ 5.4.   Commutative cyclic automata
§ 5.5.    Strongly connected quasi-automata
§ 5.6.    State independent quasi-automata
§ 5.7.    Quasi-perfect quasi-automata
§ 5.8.    Perfect quasi-automata
APPENDIX
STRUCTURAL SYSTEMS
1.  Abstract and structural automata
2.  Universal algebras
3.  Universal algebra (A2, 9T)
4.  Decompositions of operations of (A2, 91)
5.  Some special classes of operations
6.  Complete subsets of 91
7.  Prime implicants and minimizations of operations from (A2, 91)
8.  Structural automata
9.  Definition of structural systems by axioms
10.  Analysis of structural systems
11.  Synthesis of structural systems
Bibliography
Author index
Subject index

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