Domain Range Semigroups and Finite Representations

06/04/2021

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by   Jaš Šemrl, et al.

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Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class R(D,R,*) is not finitely axiomatisable, answering arXiv:1811.01712 Question 5.1. We show that any signature containing D, R, ⌣, ; but not - or · has the finite representation property, an extension of the result for ordered domain algebras {0,1,D,R, ≤, 1', ⌣,;}. We survey the results in the area of the finite representation property and raise a number of open questions.