Overview

Full Product Details

Author:   Bakhadyr Khoussainov ,  Anil Nerode
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2001 ed.
Volume:   21
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   0.884kg
ISBN:  

9780817642075

ISBN 10:   0817642072
Pages:   432
Publication Date:   08 June 2001
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Basic Notions.- 1.1 Sets.- 1.2 Sequences and Tuples.- 1.3 Functions, Relations, Operations.- 1.4 Equivalence Relations.- 1.5 Linearly Ordered Sets.- 1.6 Partially Ordered Sets.- 1.7 Graphs.- 1.8 Induction.- 1.9 Trees and König’s Lemma.- 1.10 Countable and Uncountable Sets.- 1.11 Algorithms.- 2 Finite Automata.- 2.1 Two Examples.- 2.2 Finite Automata.- 2.3 Closure Properties.- 2.4 The Myhill—Nerode Theorem.- 2.5 The Kleene Theorem.- 2.6 Generalized Finite Automata.- 2.7 The Pumping Lemma and Decidability.- 2.8 Relations and Finite Automata.- 2.9 Finite Automata with Equations.- 2.10 Monadic Second Order Logic of Strings.- 3 Büchi Automata.- 3.1 Two Examples.- 3.2 Büchi Automata.- 3.3 The Büchi Theorem.- 3.4 Complementation for Büchi Automata.- 3.5 The Complementation Theorem.- 3.6 Determinism.- 3.7 Müller Automata.- 3.8 The McNaughton Theorem.- 3.9 Decidability.- 3.10 Büchi Automata and the Successor Function.- 3.11 An Application of the McNaughton Theorem.- 4 Games Played on Finite Graphs.- 4.1 Introduction.- 4.2 Finite Games.- 4.3 Infinite Games.- 4.4 Update Games and Update Networks.- 4.5 Solving Games.- 5 Rabin Automata.- 5.1 Rabin Automata.- 5.2 Special Automata.- 5.3 Game Automata.- 5.4 Equivalence of Rabin and Game Automata.- 5.5 Terminology: Arenas, Games, and Strategies.- 5.6 The Notion of Rank.- 5.7 Open Games.- 5.8 Congruence Relations.- 5.9 Sewing Theorem.- 5.10 Can Mr. (?) Visit C Infinitely Often?.- 5.11 The Determinacy Theorem.- 5.12 Complementation and Decidability.- 6 Applications of Rabin Automata.- 6.1 Structures and Types.- 6.2 The Monadic Second Order Language.- 6.3 Satisfiability and Theories.- 6.4 Isomorphisms.- 6.5 Definability in T and Decidability of S2S.- 6.6 The Structure with ? Successors.- 6.7 Applications to LinearlyOrdered Sets.- 6.8 Application to Unary Algebras.- 6.9 Applications to Cantor’s Discontinuum.- 6.10 Application to Boolean Algebras.

Reviews

The aim of this book is to present a theory of several types of automata and applications of these facts in logic, concurrency and algebra. ...The book contains suitable material for a two-semester course for students of computer science or mathematics. It is completely self-contained and one can really enjoy reading it. It is strongly recommended for researchers and postgraduate students interested in logic, automata and/or concurrency. <p>--EMS

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