Automatic presentations and semigroups

An automatic presentation is a description of a relational structures using regular languages. Informally, an automatic presentation consists of a regular language of abstract representatives for the elements of the structure, such that each relation (of arity n, say) can be recognized by a synchronous n-tape automaton. The concept, which arose from computer scientists' need to extend finite model theory to infinite structures, has only recently been applied to algebraic stuctures. This talk will introduce and survey automatic presentations, particularly for semigroups. In particular, it will discuss: (1) classifications of those semigroups of certain classes that admit automatic presentations; (2) the interaction of automatic presentations and various semigroup constructions; and (3) decision problems.