Automatic Presentations and Semigroup Constructions

atic presentation for a relational structure is, informally, an abstract representation of the elements of that structure by means of a regular language such that the relations can all be recognized by finite automata. A structure admitting an automatic presentation is said to be FA-presentable. This paper studies the interaction of automatic presentations and certain semigroup constructions, namely: direct products, free products, finite Rees index extensions and subsemigroups, strong semilattices of semigroups, Rees matrix semigroups, Bruck–Reilly extensions, zero-direct unions, semidirect products, wreath products, ideals, and quotient semigroups. For each case, the closure of the class of FA-presentable semigroups under that construction is considered, as is the question of whether the FA-presentability of the semigroup obtained from such a construction implies the FA-presentability of the original semigroup[s]. Classifications are also given of the FA-presentable finitely g...

• Type: Journal
• Year: 2010
• Where: MST
• Authors: Alan J. Cain, Graham P. Oliver, Nikola Ruskuc, Richard M. Thomas
• Keywords: Automatic Presentations, Clifford Semigroups, MST 2010, Semigroups