Automata Theory and its Applications: 21 (Progress in Computer Science and Applied Logic, 21) - Hardcover

Khoussainov, Bakhadyr; Nerode, Anil

Hardcover

ISBN 10: 0817642072 ISBN 13: 9780817642075

Publisher: Birkhäuser, 2001

Synopsis

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. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us­ ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.

About this title

Review

"The aim of this book is to present a theory of several types of automata and applications of these facts in logic, concurrency and algebra. ...The book contains suitable material for a two-semester course for students of computer science or mathematics. It is completely self-contained and one can really enjoy reading it. It is strongly recommended for researchers and postgraduate students interested in logic, automata and/or concurrency."

--EMS

Synopsis

Automata and Their Applications is a uniform treatment of the theory of finite state machines on finite and infinite strings and trees. Many books deal with automata on finite strings, but there are very few expositions that prove the fundamental results of automata on infinite strings and trees. These results have important applications to modeling parallel computation and concurrency, the specification and verification of sequential and concurrent programs, databases, operating systems, computational complexity, and decision methods in logic and algebra. Thus, this textbook fills an important gap in the literature. Beginning with coverage of all standard fundamental results regarding finite automata, the book deals Buchi and Rabin automata and their applications to operating systems, temporal logic and communication systems, as well as to various logical theories. The book is self-contained with numerous examples, illustrations, exercises, and is suitable for a two-semester undergraduate course or a one-semester graduate course/seminar.

Since no advanced mathematical background is required, the text is also useful for self-study by computer science professionals who wish to understand the foundations of modern formal approaches to software development, validation, and verification.

Edition details

• Publisher: Birkhäuser
• Publication date: 2001
• Language: English
• ISBN 10: 0817642072
• ISBN 13: 9780817642075
• Binding: Hardcover
• Number of pages: 446