This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.

This volume contains the proceedings of the 15th Spring School of the LITP (Laboratoire d'Informatique ThA(c)orique et de Programmation, UniversitA(c) Paris VI-VII, CNRS) held from May 25 to 29, 1987 in Saint-Pierre d'OlA(c)ron. The meeting was organized by M. Borillo, M. Gross, M. Nivat and D. Perrin. The purpose of this yearly meeting is to present the state of the art in a specific topic which has gained considerable maturity. The proceedings of the last three Spring Schools have already been published in this series and deal with "Automata on Infinite Words" (LNCS 192), "Combinators and Functional Programming Languages" (LNCS 242) and "Automata Networks" (LNCS 316). The contributions gathered for the 1987 conference present a unique combination of automata theory on the one hand and natural language processing on the other hand. Both fields have strong historical links as exemplified by the works of Chomsky and Harris in Linguistics, the work of Backus and others in Computer Science and the work of SchA1/4tzenberger in Algebra. The methods described and discussed in the field of string processing and automata cover the traditional algorithms for string matching, data compression, sequence comparison and lexical analysis. The papers that deal more directly with natural language processing treat automated text generation, lexical analysis and formal representation.

This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition - with full proofs - of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.

This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.