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.

Semigroups, Automata, Universal Algebra, Varieties

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.

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

This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.

This volume presents the proceedings of the Sixth International Joint Conference on the Theory and Practice of Software Engineering, TAPSOFT '95, held in Aarhus, Denmark in May 1995. TAPSOFT '95 celebrates the 10th anniversary of this conference series started in Berlin in 1985 to bring together theoretical computer scientists and software engineers (researchers and practitioners) with a view to discussing how formal methods can usefully be applied in software development. The volume contains seven invited papers, among them one by Vaugham Pratt on the recently revealed bug in the Pentium chip, and 44 revised full papers selected from a total of 147 submissions. In addition the TAPSOFT '95 proceedings contains 10 tool descriptions.

J. Richard Biichi is well known for his work in mathematical logic and theoretical computer science. (He himself would have sharply objected to the qualifier "theoretical," because he more or less identified science and theory, using "theory" in a broader sense and "science" in a narrower sense than usual.) We are happy to present here this collection of his papers. I (DS)1 worked with Biichi for many years, on and off, ever since I did my Ph.D. thesis on his Sequential Calculus. His way was to travel locally, not globally: When we met we would try some specific problem, but rarely dis cussed research we had done or might do. After he died in April 1984 I sifted through the manuscripts and notes left behind and was dumbfounded to see what areas he had been in. Essentially I knew about his work in finite au tomata, monadic second-order theories, and computability. But here were at least four layers on his writing desk, and evidently he had been working on them all in parallel. I am sure that many people who knew Biichi would tell an analogous story.

This collection of articles is unique in the way it approaches established material on the various logical traditions in India. Instead of classifying these traditions within Schools as is the usual approach, the material here is classified into sections based on themes ranging from Fundamentals of ancient logical traditions to logic in contemporary mathematics and computer science. This collection offers not only an introduction to the key themes in different logical traditions such as Nyaya, Buddhist and Jaina, it also highlights certain unique characteristics of these traditions as well as contribute new material in the relationship of logic to aesthetics, linguistics, Kashmir Saivism as well as the forgotten Tamil contribution to logic.

A collection of articles by leading experts in theoretical computer science, this volume commemorates the 75th birthday of Professor Rani Siromoney, one of the pioneers in the field in India. The articles span the vast range of areas that Professor Siromoney has worked in or influenced, including grammar systems, picture languages and new models of computation.