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Well Quasi-Orders Arising from Finite Ordered Semigroups

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Developments in Language Theory (DLT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13257))

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Abstract

In 1985, Bucher, Ehrenfeucht and Haussler studied derivation relations associated with a given set of context-free rules. Their research motivated a question regarding homomorphisms from the semigroup of all words onto a finite ordered semigroup. The question is which of these homomorphisms induce a well quasi-order on the set of all words. We show that this problem is decidable and the answer does not depend on the homomorphism, but it is a property of the ordered semigroup.

The research was supported by Grant 19-12790S of the Grant Agency of the Czech Republic.

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Notes

  1. 1.

    For a variant of Higman’s Lemma where the alphabet A is equipped with the quasi-order \(\preceq \), we take for the ordered semigroup S the subsemigroup of P(A) consisting of all downward closed subsets of A with respect to the considered quasi-order \(\preceq \). Note that for an infinite alphabet the constructed ordered semigroup is not finite and therefore it is not our focus.

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Acknowledgement

We are grateful to the referees for their numerous valuable suggestions which improved the paper, in particular, its introductory part. We also thank to Michal Kunc for inspiring discussions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Ondřej Klíma & Jonatan Kolegar

Authors
  1. Ondřej Klíma
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  2. Jonatan Kolegar
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Correspondence to Ondřej Klíma .

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Editors and Affiliations

  1. University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Volker Diekert

  2. Ural Federal University, Ekaterinburg, Russia

    Mikhail Volkov

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Klíma, O., Kolegar, J. (2022). Well Quasi-Orders Arising from Finite Ordered Semigroups. In: Diekert, V., Volkov, M. (eds) Developments in Language Theory. DLT 2022. Lecture Notes in Computer Science, vol 13257. Springer, Cham. https://doi.org/10.1007/978-3-031-05578-2_16

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  • DOI: https://doi.org/10.1007/978-3-031-05578-2_16

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  • Print ISBN: 978-3-031-05577-5

  • Online ISBN: 978-3-031-05578-2

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