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Domain Range Semigroups and Finite Representations

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Relational and Algebraic Methods in Computer Science (RAMiCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13027))

Abstract

Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class of domain-range semigroups with demonic composition is not finitely axiomatisable. We extend the result for ordered domain algebras and show that any relation algebra reduct signature containing domain, range, converse, and composition, but no negation, meet, nor join has the finite representation property. That is any finite representable structure of such a signature is representable over a finite base. We survey the results in the area of the finite representation property.

J. Šemrl—The author thanks Professor Robin Hirsch for supervision and insightful conversations about the work presented.

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Authors and Affiliations

  1. University College London, Gower Street, London, WC1E 6BT, UK

    Jaš Šemrl

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  1. Jaš Šemrl
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Correspondence to Jaš Šemrl .

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Editors and Affiliations

  1. École polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Université Côte d’Azur, Nice, France

    Mai Gehrke

  3. Aix-Marseille University, Marseille, France

    Luigi Santocanale

  4. Brock University, St Catharines, ON, Canada

    Michael Winter

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Šemrl, J. (2021). Domain Range Semigroups and Finite Representations. In: Fahrenberg, U., Gehrke, M., Santocanale, L., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2021. Lecture Notes in Computer Science(), vol 13027. Springer, Cham. https://doi.org/10.1007/978-3-030-88701-8_29

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  • DOI: https://doi.org/10.1007/978-3-030-88701-8_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-88700-1

  • Online ISBN: 978-3-030-88701-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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