Infinite words : automata, semigroups, logic and games /

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theo...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Perrin, Dominique
Otros Autores: Pin, Jean Eric
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier, 2004.
Edición:1st ed.
Colección:Pure and applied mathematics (Academic Press) ; 141.
Temas:
Machine theory.
Group theory.
Th�eorie des automates.
Th�eorie des groupes.
MATHEMATICS > Group Theory.
Automatentheorie.
Speltheorie.
Logica.
Groepentheorie.
Topologie.
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Tabla de Contenidos:
  • Cover
  • Contents
  • Preface
  • Chapter I. AUTOMATA AND INFINITE WORDS
  • 1. Introduction
  • 2. Words and trees
  • 3. Rational sets of infinite words
  • 4. Automata
  • 5. B�uchi automata
  • 6. Deterministic B�uchi automata
  • 7. Muller and Rabin automata
  • 8. Transition automata
  • 9. McNaughton's theorem
  • 10. Computational complexity issues
  • 11. Exercises
  • 12. Notes
  • Chapter II. AUTOMATA AND SEMIGROUPS
  • 1. Introduction
  • 2. Ramseyan factorizations and linked pairs
  • 3. Recognition by morphism
  • 4. Semigroups and infinite products
  • 5. Wilke Algebras
  • 6. Recognition by morphism of?-semigroups
  • 7. The two modes of recognition
  • 8. Syntactic congruence
  • 9. Back to McNaughton's theorem
  • 10. Prophetic automata
  • 11. Exercises
  • 12. Notes
  • Chapter III. AUTOMATA AND TOPOLOGY
  • 1. Introduction
  • 2. Topological spaces
  • 3. The space of infinite words
  • 4. The space of finite or infinite words
  • 5. Borel automata
  • 6. Suslin sets
  • 7. The separation theorem
  • 8. Exercises
  • 9. Notes
  • Chapter IV. GAMES AND STRATEGIES
  • 1. Introduction
  • 2. Infinite games
  • 3. Borel games
  • 4. Games on graphs
  • 5. Wadge games
  • 6. Exercises
  • 7. Notes
  • Chapter V. WAGNER HIERARCHY
  • 1. Introduction
  • 2. Ordinals
  • 3. Classes of sets
  • 4. Chains
  • 5. Superchains
  • 6. The Wagner hierarchy
  • 7. Exercises
  • 8. Notes
  • Chapter VI. VARIETIES
  • 1. Introduction
  • 2. Varieties of finite or infinite words
  • 3. Varieties and topology
  • 4. Weak recognition
  • 5. Extensions of McNaughton's theorem
  • 6. Varieties closed under aperiodic extension
  • 7. Concatenation hierarchies for infinite words
  • 8. Exercises
  • 9. Notes
  • Chapter VII. LOCAL PROPERTIES
  • 1. Introduction
  • 2. Weak recognition
  • 3. Local properties of infinite words
  • 4. Exercises
  • 5. Notes
  • Chapter VIII. AN EXCURSION INTO LOGIC
  • 1. Introduction
  • 2. The formalism of logic
  • 3. Monadic second-order logic on words
  • 4. First-order logic of the linear order
  • 5. First-order logic of the successor
  • 6. Temporal logic
  • 7. Restricted temporal logic
  • 8. Exercises
  • 9. Notes
  • Chapter IX. BI-INFINITE WORDS
  • 1. Introduction
  • 2. Bi-infinite words
  • 3. Determinism
  • 4. Morphisms
  • 5. Unambiguous automata on bi-infinite words
  • 6. Discrimination
  • 7. Logic on Z
  • 8. Exercises
  • 9. Notes
  • Chapter X. INFINITE TREES
  • 1. Introduction
  • 2. Finite and Infinite trees
  • 3. Tree automata
  • 4. Tree automata and games
  • 5. Topology
  • 6. Monadic second order logic of two successors
  • 7. Effective algorithms
  • 8. Exercises
  • 9. Notes
  • ANNEX A. FINITE SEMIGROUPS
  • 1. Monoids.

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