Finite Automata, Their Algebras and Grammars

1. Front Matter

   Pages i-xxii

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2. Concepts and Notations in Discrete Mathematics

   • J. Richard Büchi, Dirk Siefkes

   Pages 1-75

3. The Structure Theory of Transition Algebras

   • J. Richard Büchi, Dirk Siefkes

   Pages 76-105

4. The Structure and Behavior of Finite Automata

   • J. Richard Büchi, Dirk Siefkes

   Pages 106-132

5. Transition Systems and Regular Events

   • J. Richard Büchi, Dirk Siefkes

   Pages 133-179

6. Regular Canonical Systems

   • J. Richard Büchi, Dirk Siefkes

   Pages 180-216

7. General Algebras: How They Function as Tree Acceptors and Push-down Automata

   • J. Richard Büchi, Dirk Siefkes

   Pages 217-270

8. General Alphabets: The Theory of Push-down Automata and Context-free Languages

   • J. Richard Büchi, Dirk Siefkes

   Pages 271-292

9. Conclusion

   • J. Richard Büchi, Dirk Siefkes

   Pages 292-292

10. Back Matter

    Pages 293-316

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The author, who died in 1984, is well-known both as a person and through his research in mathematical logic and theoretical computer science. In the first part of the book he presents the new classical theory of finite automata as unary algebras which he himself invented about 30 years ago. Many results, like his work on structure lattices or his characterization of regular sets by generalized regular rules, are unknown to a wider audience. In the second part of the book he extends the theory to general (non-unary, many-sorted) algebras, term rewriting systems, tree automata, and pushdown automata. Essentially Büchi worked independent of other rersearch, following a novel and stimulating approach. He aimed for a mathematical theory of terms, but could not finish the book. Many of the results are known by now, but to work further along this line presents a challenging research program on the borderline between universal algebra, term rewriting systems, and automata theory. For the whole book and again within each chapter the author starts at an elementary level, giving careful explanations and numerous examples and exercises, and then leads up to the research level. In this way he covers the basic theory as well as many nonstandard subjects. Thus the book serves as a textbook for both the beginner and the advances student, and also as a rich source for the expert.

• Alphabet
• Lattice
• automata
• automata theory
• grammars
• logic
• mathematical logic
• combinatorics

• Fachbereich Informatik, Technische Universität Berlin, Berlin, Federal Republic of Germany

  Dirk Siefkes

• Computer Science Department, Purdue University, West Lafayette, USA

  J. Richard Büchi

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