This research is concerned with a study of algorithmic problems in the theories of groups, semigroups, inverse semigroups and associative algebras. Related problems about automata, varieties and pseudo-varieties will also be considered. Algorithmic problems to be considered include the word problem for non-periodic semigroup varieties, for finitely based varieties of associative algebras, for presentations and varieties of inverse semigroups. Other problems to be considered include the algorithmic classification of finitely generated subgroups of free groups via finite inverse monoids, the Rhodes problem for the class of finite groups and the extension problem for finite inverse automata to various pseudo-varieties of groups. This research is in the area of semigroups. A semigroup is one of the simplest of the abstract mathematical structures, consisting of a set with one associative operation on it. The structure of these very general objects will be investigated. Applications will be given to various areas of mathematics and computer science.
