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

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Title: Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited
Authors: Ballester Bolinches, Adolfo | Pin, Jean-Éric | Soler Escrivà, Xaro
Research Group/s: Grupo de Álgebra y Geometría (GAG)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Group formations | Regular languages | Semigroups | Automata theory
Knowledge Area: Álgebra
Issue Date: Nov-2014
Publisher: De Gruyter
Citation: Forum Mathematicum. 2014, 26(6): 1737-1761. doi: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.
Sponsor: The authors are supported by Proyecto MTM2010-19938-C03-01 from MICINN (Spain). The second author is supported by the project ANR 2010 BLAN 0202 02 FREC. The third author was supported by the Grant PAID-02-09 from Universitat Politècnica de València.
ISSN: 0933-7741 (Print) | 1435-5337 (Online)
DOI: 10.1515/forum-2012-0055
Language: eng
Type: info:eu-repo/semantics/article
Rights: © de Gruyter 2014
Peer Review: si
Publisher version:
Appears in Collections:INV - GAG - Artículos de Revistas

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