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The homomorphism problem for the free monoid

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 2002 English Publisher:Elsevier BVJournal:Discrete Mathematics, volume 259, pages 189-200 (issn: 0012-365X, Copyright policy )
Authors: Pedro V. Silva;

doi: 10.1016/s0012-365x(02)00380-1

The homomorphism problem for the free monoid

Abstract

The following extension problem for mappings is shown to be algorithmically decidable: given a finite subset \(F\) of words over an alphabet \(X\) and a mapping \(\varphi\colon F\to X^*\), determine whether or not \(\varphi\) can be extended to a monoid homomorphism \(F^*\to X^*\). This result gives another solution to the isomorphism problem for finitely generated submonoids of free monoids, a result due to \textit{C. Choffrut, T. Harju}, and \textit{J. Karhumäki} [Theor. Comput. Sci. 183, No. 1, 83-92 (1997; Zbl 0901.68096)].

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Keywords

Free semigroups, generators and relations, word problems, Combinatorics on words, isomorphism problem, decidability, Free monoid, Decidability, homomorphism problem, free monoids, Theoretical Computer Science, Homomorphism, Mappings of semigroups, Discrete Mathematics and Combinatorics, Isomorphism

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
hybrid