Automatic presentations and semigroup constructions
MetadataShow full item record
An automatic 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 generated Clifford semigroups, completely simple semigroups, and completely 0-simple semigroups.
Cain , A J , Oliver , G , Ruskuc , N & Thomas , R M 2010 , ' Automatic presentations and semigroup constructions ' Theory of Computing Systems , vol. 47 , no. 2 , pp. 568-592 . DOI: 10.1007/s00224-009-9216-4
Theory of Computing Systems
This is an author version of this article. The original publication, (c) Springer Science+Business Media, LLC 2009, is available at www.springerlink.com
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.