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Automata Theory and its Applications

The theory of finite automata on finite stings, infinite strings, and trees has had a dis­ tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950...

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Bibliographic Details
Main Authors: Khoussainov, Bakhadyr, Nerode, Anil (Author)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 2001, 2001
Edition:1st ed. 2001
Series:Progress in Computer Science and Applied Logic
Subjects:
Software Engineering
Computer Science
Mathematical Logic
Artificial Intelligence
Formal Languages And Automata Theory
Machine Theory
Theory Of Computation
Mathematical Logic And Foundations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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

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