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Home > Computing and Information Technology > Computer science > Mathematical theory of computation > Finite Automata, Formal Logic, and Circuit Complexity: (Progress in Theoretical Computer Science)
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Finite Automata, Formal Logic, and Circuit Complexity: (Progress in Theoretical Computer Science)

Finite Automata, Formal Logic, and Circuit Complexity: (Progress in Theoretical Computer Science)


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About the Book

This work, intended for researchers and advanced students in theoretical computer science and mathematics, is situated at the juncture of automata theory, logic, semigroup theory and computational complexity. The first part focuses on the algebraic characterization of the regular languages definable in many different logical theories. The second part presents the recently-discovered connections between the algebraic theory of automata and the complexity theory of small-depth circuits. The first seven chapters of this text are devoted to the algebraic characterization of the regular languages definable in many different logical theories, obtained by varying both the kinds of quantification and the atomic formulas that are admitted. This includes the results of Buchi and of McNaughton and Papert, as well as more recent developments that are scattered throughout research journals and conference proceedings. The two tables at the end of Chapter 7 summarize most of the important results of this first part of the book. Chapter 8 provides a brief account of the complexity theory of small-depth families of boolean circuits. Chapter 9 aims to tie all the threads together: it shows that questions about the structure of complexity classes of small-depth circuits are precisely equivalent to questions about the definability of regular languages in various versions of first-order logic.

Table of Contents:
I Mathematical Preliminaries.- I.1 Words and Languages.- I.2 Automata and Regular Languages.- I.3 Semigroups and Homomorphisms.- II Formal Languages and Formal Logic.- II.1 Examples.- II.2 Definitions.- III Finite Automata.- III.1 Monadic Second-Order Sentences and Regular Languages.- III.2 Regular Numerical Predicates.- III.3 Infinite Words and Decidable Theories.- IV Model-Theoretic Games.- IV.1 The Ehrenfeucht-Fraïssé Game.- IV.2 Application to FO[


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Product Details
  • ISBN-13: 9780817637194
  • Publisher: Birkhauser Boston Inc
  • Publisher Imprint: Birkhauser Boston Inc
  • Height: 235 mm
  • No of Pages: 227
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 0817637192
  • Publisher Date: 03 May 1994
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: Progress in Theoretical Computer Science


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Finite Automata, Formal Logic, and Circuit Complexity: (Progress in Theoretical Computer Science)
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