This is a rigorous and self-contained monograph on a central topic in theoretical computer science. For the first time in book form, original results from the last ten years are presented, some previously unpublished, using combinatorial and algebraic methods. These are mainly based on combinatorics on words and especially on the theory of "unavoidable regularities." Researchers will find important new results on semigroups and formal languages, as well as various applications for these methods.

Semigroups, Formal Languages and Groups contains articles that provide introductory accounts of recent research in rational languages and their connections with finite semigroups, including the celebrated BG=PG theorem, infinite languages, free profinite monoids and their applications to pseudovarieties, parallel complexity classes related to automata, semigroups and logic, algebraic monoids, geometric methods in semigroup presentations, automatic groups and groups acting on Lambda-trees. There is also an extensive survey of algorithmic problems in groups, semigroups and inverse monoids. In addition, the book includes hitherto unpublished research on monoids of Lie type and their representations, free actions of groups on Lambda-trees and an extension to arbitrary semigroups of the famous Krohn-Rhodes theorem.

This festschrift volume in honour of Donald B McAlister on the occasion of his 65th birthday presents papers from leading researchers in semigroups and formal languages. The contributors cover a number of areas of current interest: from pseudovarieties and regular languages to ordered groupoids and one-relator groups, and from semigroup algebras to presentations of monoids and transformation semigroups. The papers are accessible to graduate students as well as researchers seeking new directions for future work.

This festschrift volume in honour of Donald B McAlister on the occasion of his 65th birthday presents papers from leading researchers in semigroups and formal languages. The contributors cover a number of areas of current interest: from pseudovarieties and regular languages to ordered groupoids and one-relator groups, and from semigroup algebras to presentations of monoids and transformation semigroups. The papers are accessible to graduate students as well as researchers seeking new directions for future work.

This festschrift volume in honour of Donald B McAlister on the occasion of his 65th birthday presents papers from leading researchers in semigroups and formal languages. The contributors cover a number of areas of current interest: from pseudovarieties and regular languages to ordered groupoids and one-relator groups, and from semigroup algebras to presentations of monoids and transformation semigroups. The papers are accessible to graduate students as well as researchers seeking new directions for future work.

This book is based on notes for a master’s course given at Queen Mary, University of London, in the 1998/9 session. Such courses in London are quite short, and the course consisted essentially of the material in the ?rst three chapters, together with a two-hour lecture on connections with group theory. Chapter 5 is a considerably expanded version of this. For the course, the main sources were the books by Hopcroft and Ullman ([20]), by Cohen ([4]), and by Epstein et al. ([7]). Some use was also made of a later book by Hopcroft and Ullman ([21]). The ulterior motive in the ?rst three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Three such notions are considered. These are: generated by a type 0 grammar, recognised by a Turing machine (deterministic or not) and de?ned by means of a Godel ̈ numbering, having de?ned “recursively enumerable” for sets of natural numbers. It is hoped that this has been achieved without too many ar- ments using complicated notation. This is a problem with the entire subject, and it is important to understand the idea of the proof, which is often quite simple. Two particular places that are heavy going are the proof at the end of Chapter 1 that a language recognised by a Turing machine is type 0, and the proof in Chapter 2 that a Turing machine computable function is partial recursive.

The proceedings present some new topics and techniques of semigroup theory. Papers by leading experts in this theory are collected. Since results on semigroups have naturally been employed in formal languages and codes, the focus is also on these directions.