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Free group languages: Rational versus recognizable

Published online by Cambridge University Press:  15 March 2004

Pedro V. Silva
Pedro V. Silva*
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. do Campo Alegre, 687, 4169-007 Porto, Portugal; pvsilva@fc.up.pt.
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Abstract

We provide alternative proofs and algorithms for resultsproved by Sénizergues on rational and recognizable freegroup languages. We consider two different approaches to the basicproblem of deciding recognizability for rational free group languagesfollowing two fully independent paths: the symmetrificationmethod (using techniques inspired by the study ofinverse automata and inverse monoids) andthe right stabilizer method (a general approach generalizable to otherclasses of groups). Several different algorithmic characterizations ofrecognizability are obtained, as well as other decidability results.

Keywords

Free grouprational subsetsrecognizable subsets.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 1 , January 2004 , pp. 49 - 67
Copyright
© EDP Sciences, 2004

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References

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Sénizergues, G., On the rational subsets of the free group. Acta Informatica 33 (1996) 281-296. CrossRef
Silva, P.V., On free inverse monoid languages. RAIRO: Theoret. Informatics Appl. 30 (1996) 349-378.
Silva, P.V., Recognizable subsets of a group: finite extensions and the abelian case. Bulletin of the EATCS 77 (2002) 195-215.