Semigroups, Formal Languages and Groups

This volume 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 -trees. There is also an extensive survey of algorithm ic 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 In addition, the book includes hitherto unpublished research on monoids of Lie type and their representations, free actions of groups on -trees and an extension to arbitrary semigroups of the famous Krohn-Rhodes theorem.