Paper “Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited” published in Forum Math.

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Adolfo Ballester-Bolinches, Jean-Éric Pin, Xaro Soler-Escrivà

Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited

Forum Math., 26(6) (2014), 1737–1761

http://dx.doi.org/10.1515/forum-2012-0055

Abstract

We present an extension of Eilenberg’s variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.

2010 Mathematics subject classification: 20D10; 20M35

KeywordsGroup formations; regular languages; semigroups; automata theory