| Edition |
1st ed. |
| Description |
1 online resource (xi, 538 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Pure and applied mathematics series ; 141 |
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Pure and applied mathematics (Academic Press) ; 141.
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| 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 Schätzenberger. 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. |
| Note |
"Academic Press." |
| Bibliography |
Includes bibliographical references (pages 499-521). |
| Note |
Print version record. |
| 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. Büchi automata -- 6. Deterministic Büchi 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. |
| Subject |
Machine theory.
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Group theory.
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Théorie des automates.
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Théorie des groupes.
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MATHEMATICS -- Group Theory.
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Group theory
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Machine theory
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Automatentheorie.
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Speltheorie.
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Logica.
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Groepentheorie.
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Topologie.
|
| Added Author |
Pin, Jean Eric.
|
| Other Form: |
Print version: Perrin, Dominique. Infinite words. 1st ed. Amsterdam ; Boston : Elsevier, 2004 0125321112 9780125321112 (DLC) 2006277681 (OCoLC)51914111 |
| ISBN |
9780125321112 |
|
0125321112 |
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9780080525648 (electronic bk.) |
|
0080525644 (electronic bk.) |
| Standard No. |
AU@ 000048129788 |
|
AU@ 000062575602 |
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CHDSB 005989083 |
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CHNEW 001007036 |
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DEBBG BV036962377 |
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DEBBG BV042317362 |
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DEBSZ 276801180 |
|
DEBSZ 482357002 |
|
NZ1 12433774 |
|
NZ1 15192914 |
|
