Finite Automata, Formal Logic, and Circuit Complexity (Progress in Theoretical Computer Science) - Tapa dura

Straubing, Howard

 
9780817637194: Finite Automata, Formal Logic, and Circuit Complexity (Progress in Theoretical Computer Science)
Tapa dura
ISBN 10: 0817637192 ISBN 13: 9780817637194
Editorial: Birkhäuser, 1994

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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.

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
1994
Idioma
Inglés
ISBN 10 
0817637192
ISBN 13 
9780817637194
Encuadernación
Tapa dura
Número de páginas
240
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9781461266952: Finite Automata, Formal Logic, and Circuit Complexity (Progress in Theoretical Computer Science)

Edición Destacada

ISBN 10:  1461266955 ISBN 13:  9781461266952
Editorial: Birkhäuser, 2012
Tapa blanda