UID:
almafu_9958085680002883
Umfang:
1 online resource (403 p.)
ISBN:
1-281-76346-2
,
9786611763466
,
0-08-087375-8
Serie:
Pure and Applied Mathematics. A Series of Monographs and Textbooks
Inhalt:
Automata, languages, and machines
Anmerkung:
Description based upon print version of record.
,
Front Cover; Automata, Languages, and Machines; Copyright Page; Contents; Preface; Chapter I. Transformation Semigroups; 1. Semigroups, Monoids, and Groups; 2. Transformation Semigroups; 3. Examples of Transformation Semigroups; 4. Coverings; 5. Coverings of Semigroups; 6. Inclusions and Restrictions; 7. Isomorphisms and Equivalences; 8. Join, Sum, and Direct Product; 9. Some Simple Inequalities; 10. The Wreath Product; References; Chapter II. Decomposition Theorems; 1. Decompositions; 2. Decomposition of Groups; 3. Some UsefuI Decompositions; 4. The Krohn-Rhodes Decomposition
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5. Comments on the Proof6. Height, Pavings, and Holonomy; 7. The Holonomy Decomposition Theorem; 8. Proof of Proposition 7.3; 9. Examples; References; Chapter III. Transformation Semigroups (continued); 1. Classes and Closed Classes; 2. Sinks in a ts; 3. Transitivity Classes; 4. Idempotents in Semigroups; 5. Idempotents in a ts; 6. Localization; 7. Closed Classes Containing 2; 8. The Derived ts and the Trace of a Covering; 9. The Delay Covering; References; Chapter IV. Primes; 1. The Exclusion Operator; 2. Primes; 3. Proof of Theorem 2.1; 4. The Low Primes; 5. The Primes C and C ̇
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6. The Primes F, 2, F ̇, and 2 ̇7. Switching Rules; 8. Summary and Open Problems; References; Chapter V Semigroups and Varieties; 1. Varieties of Semigroups and Monoids; 2. Varieties Defined by Equations; 3. Examples of Ultimately Equational Varieties; 4. Semidirect Products; 5. Varieties V.W; 6. Varieties vs. Weakly Closed Classes; 7. Closed Varieties; 8. Examples of Closed Varieties; 9. Triple Products; 10. G-Varieties; 11. Primes; 12. A Tabulation; References; Chapter VI. Decomposition of Sequential Functions; 1. Syntactic Invariants of Sequential Functions; 2. Composition; 3. Decomposition
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4. Parallel Composition5. Examples of Decompositions; 6. The Function Š; 7. Varieties of Sequential Functions; Chapter VII. Varieties of Sets; 1. Syntactic Semigroups; 2. Syntactic Semigroups and Recognizable Sets; 3. Varieties of Sets; 4. Proof of Theorems 3.2 and 3.2s; 5. Operations on Varieties; 6. The Syntactic tm and ts of a Set; Chapter VIII. Examples of Varieties of Sets; 1. General Comments; 2. Finite and Cofinite Sets; 3. Finitely Generated Varieties; 4. The Variety D; 5. The Variety D; 6. Locally Testable Sets; 7. A Theorem on Graphs; 8. Proof of Theorem 6.5; 9. The *-Variety j
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10. p-GroupsReferences; Chapter IX. Aperiodicity; 1. Recognizable Sets and Sequential Functions; 2. The Concatenation Product; 3. Schützenberger's Theorem; 4. The Brzozowski Hierarchy; 5. Bn,1 Are +-Varieties; 6. The Variety B2; 7. The Variety A1; References; Chapter X. Unitary-Prefix Decompositions; 1. Unitary-Prefix Decompositions; 2. A Decomposition; 3. Two Examples; 4. Iterated Decomposition; 5. Periods of Monoids; 6. Proof of Theorem 5.2; References; Chapter XI. Depth Decomposition Theorem; 1. Basic Orderings in Semigroups; 2. The Depth Decomposition Theorem; 3. The Rees Matrix Semigroup
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4. The Reduction Theorem
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English
Weitere Ausg.:
ISBN 0-12-234002-7
Sprache:
Englisch
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