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2010

Automatic Presentations and Semigroup Constructions

11 years 3 months ago
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...
Alan J. Cain, Graham P. Oliver, Nikola Ruskuc, Ric
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where MST
Authors Alan J. Cain, Graham P. Oliver, Nikola Ruskuc, Richard M. Thomas
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