An automatic presentation (also called an FA-presentation) is a description of a relational structure using regular languages. The concept an FA-presentation arose in computer science, to fulfil a need to extend finite model theory to infinite structures. Informally, an FA-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.

In this talk, I will give a brief introduction to automatic presentations, with a particular focus on how they apply to groups and semigroups. I will then discuss whether certain decision problems are solvable within the classes of groups and semigroups with automatic presentations.