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Journals ACM SIGACT News Volume 25 Issue 3

BOOK REVIE W Finite Automata, Formal Logic, and Circuit Complexity . By Howard Straubing . Birkhauser . 1994 . xii+226pp . ISBN 0-8176-3719-2 . $39 .50 . 1. Overview This is a very focused book . The book's main focus is on expressibility : given a logical language , which sets of strings can be expressed in it? The author brings in other topics such as circui t complexity and monoids, but it is all used to prove results about expressibility . Expressibility is an important theme in Computer Science and Logic . Biichi [7] used it to obtain decidability results . Fagin [9] characterized NP in terms of expressibility . Immerman has spend most of his adult life characterizing classes in this manner . He was lead to the proof tha t NSPACE(S(n)) is closed under complementation [11] . Papadimitriou and Yannakakis [15] hav e used expressibility to define classes of problems related to approximations . This book ties together finite automata, algebraic theory of automata, formal logic, expressibility, circuits, and abstract algebra . Thus it should be of interest to anyone interested in any one o f those fields . The book is self-contained so no

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BOOK REVIEW: Finite Automata, Formal Logic, and Circuit Complexity. By Howard Straubing. (Birkhauser. 1994. xii+226pp. ISBN 0-8176-3719-2. $39.50.)

Reviewer-Gasarch, William
ACM SIGACT News , Volume 25 (3)
Association for Computing Machinery – Sep 1, 1994

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