Finite Automata

Finite Automata

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Interest in finite automata theory continues to grow, not only because of its applications in computer science, but also because of more recent applications in mathematics, particularly group theory and symbolic dynamics. The subject itself lies on the boundaries of mathematics and computer science, and with a balanced approach that does justice to both aspects, this book provides a well-motivated introduction to the mathematical theory of finite automata. The first half of Finite Automata focuses on the computer science side of the theory and culminates in Kleene's Theorem, which the author proves in a variety of ways to suit both computer scientists and mathematicians. In the second half, the focus shifts to the mathematical side of the theory and constructing an algebraic approach to languages. Here the author proves two main results: Schutzenberger's Theorem on star-free languages and the variety theorem of Eilenberg and Schutzenberger. Accessible even to students with only a basic knowledge of discrete mathematics, this treatment develops the underlying algebra gently but rigorously, and nearly 200 exercises reinforce the concepts. Whether your students' interests lie in computer science or mathematics, the well organized and flexible presentation of Finite Automata provides a route to understanding that you can tailor to their particular tastes and abilities.show more

Product details

  • Hardback | 320 pages
  • 162.1 x 240.8 x 22.4mm | 589.68g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 176 black & white illustrations, 33 black & white tables
  • 1584882557
  • 9781584882558

Review quote

"Lawson's book is well written, self-contained, and quite extensive. The material is fully explained, with many examples fully discussed, and with many and varied exercises. Students using this book will get a broad education in finite-automata theory." - SIAM Review "[This book] is a nice textbook intended for an undergraduate lecture. All presented results are illustrated by many simple examples. The book is self-contained and easy to read. It can be recommended as a textbook for undergraduate lectures about finite automata." - EMS Newslettershow more

Table of contents

INTRODUCTION TO FINITE AUTOMATA Alphabets and Strings Languages Language Operations Finite Automata: Motivation Finite Automata and their Languages Summary of Chapter 1 Remarks on Chapter 1 RECOGNISABLE LANGUAGES Designing Automata Incomplete Automata Automata which Count Automate which Locate Patterns Boolean Operations The Pumping Lemma Summary of Chapter 2 Remarks on Chapter 2 NON-DETERMINISTIC AUTOMATA Accessible Automata Non-Deterministic Automata Applications Trim Automata Grammars Summary of Chapter 3 Remarks on Chapter 3 e-AUTOMATA Automata withe-Transitions Applications of e-Automata Summary of Chapter 4 Remarks on Chapter 4 KLEENE'S THEOREM Regular Languages Kleene's Theorem: Proof Kleene's Theorem: algorithms Language Equations Summary of Chapter 5 Remarks on Chapter 5 LOCAL LANGUAGES Myhill Graphs Linearisation Summary of Chapter 6 Remarks on Chapter 6 MINIMAL AUTOMATA Partitions and Equivalence Relations The Indistinguishability Relation Isomorphisms of Automata The Minimal Auomaton The Method of Quotients Summary of Chapter 7 Remarks on Chapter 7 THE TRANSITION MONOID Functions on States The Extended Transition Table The Cayley Table of an Automaton Semigroups and Monoids Summary of Chapter 8 Remarks on Chapter 8 THE SYNTACTIC MONOID Introduction to Semigroups Congruences The Transition Monoid of an Automaton The Syntactic Monoid of a Language Summary of Chapter 9 Remarks on Chapter 9 ALGEBRAIC LANGUAGE THEORY Finite Semigroups Recognisability by a Monoid Two Counterexamples Summary of Chapter 10 Remarks on Chapter 10 STAR-FREE LANGUAGES Introduction Groups Aperiodic Semigroups Schutzenberger's Theorem An Example Summary of Chapter 11 Remarks on Chapter 11 VARIETIES OF LANGUAGES Pseudovarieties and Varieties Summary of Chapter 12 Remarks on Chapter 12 APPENDIX: DISCRETE MATHEMATICS Logic and Proofs Set Theory Numbers and Matrices Graphs Functions Relations BIBLIOGRAPHY INDEXshow more