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Domain Range Semigroups and Finite Representations

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


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.


  • Domain-range semigroups
  • Demonic composition
  • Finite representation property

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

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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.

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