Screen LibraryInfinite 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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| Main Authors: | |
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| Corporate Authors: | |
| Group Author: | |
| Published: |
Elsevier,
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| Publisher Address: | Amsterdam : |
| Publication Dates: | 2004. |
| Literature type: | eBook |
| Language: | English |
| Edition: | First edition. |
| Series: |
Pure and applied mathematics series ;
141 |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/bookseries/00798169/141 |
| Summary: |
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 theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Bochi, McNaughton and Scha tzenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures. |
| Item Description: | "Academic Press." |
| Carrier Form: | 1 online resource (xi, 538 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 499-521). |
| ISBN: |
9780125321112 0125321112 9780080525648 0080525644 |
| Index Number: | QA267 |
| CLC: | TP301.6 |
| Contents: | Cover -- Contents -- Preface -- Chapter I. AUTOMATA AND INFINITE WORDS -- 1. Introduction -- 2. Words and trees -- 3. Rational sets of infinite words -- 4. Automata -- 5. Bu chi automata -- 6. Deterministic Bu chi 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. |