Finite Automata, Formal Logic, and Circuit Complexity

1. Front Matter

   Pages i-xii

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2. Mathematical Preliminaries

   • Howard Straubing

   Pages 1-8

3. Formal Languages and Formal Logic

   • Howard Straubing

   Pages 9-20

4. Finite Automata

   • Howard Straubing

   Pages 21-37

5. Model-Theoretic Games

   • Howard Straubing

   Pages 39-52

6. Finite Semigroups

   • Howard Straubing

   Pages 53-78

7. First-Order Logic

   • Howard Straubing

   Pages 79-98

8. Modular Quantifiers

   • Howard Straubing

   Pages 99-126

9. Circuit Complexity

   • Howard Straubing

   Pages 127-153

10. Regular Languages and Circuit Complexity

    • Howard Straubing

    Pages 155-178

11. Back Matter

    Pages 179-227

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The study of the connections between mathematical automata and for­ mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first­ order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log­ ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup­ theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor­ mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com­ puter science community, which moved to other concerns.

• algorithms
• automata
• complexity
• computer
• computer science
• formal language
• formal languages
• formal logic
• logic
• predicate logic
• theoretical computer science

• Computer Science Department, Boston College, Chestnut Hill, USA

  Howard Straubing

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