License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2020.29
URN: urn:nbn:de:0030-drops-128411
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12841/
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Doumane, Amina ; Pous, Damien

Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms

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Abstract

We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation). Without these constants, the equational theory coincides with that of semilattice-ordered semigroups. We show that the equational theory is no longer finitely based when adding one or the other constant, refuting a conjecture from the literature. Our proofs exploit a characterisation in terms of graphs and homomorphisms, which we show how to adapt in order to capture standard equational theories over the considered signatures.

BibTeX - Entry

@InProceedings{doumane_et_al:LIPIcs:2020:12841,
  author =	{Amina Doumane and Damien Pous},
  title =	{{Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Igor Konnov and Laura Kov{\'a}cs},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12841},
  URN =		{urn:nbn:de:0030-drops-128411},
  doi =		{10.4230/LIPIcs.CONCUR.2020.29},
  annote =	{Keywords: Relation algebra, graph homomorphisms, (in)equational theories}
}

Keywords: Relation algebra, graph homomorphisms, (in)equational theories
Collection: 31st International Conference on Concurrency Theory (CONCUR 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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