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.2018.18
URN: urn:nbn:de:0030-drops-95564
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9556/
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Doumane, Amina ; Pous, Damien

Completeness for Identity-free Kleene Lattices

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LIPIcs-CONCUR-2018-18.pdf (0.6 MB)

Abstract

We provide a finite set of axioms for identity-free Kleene lattices, which we prove sound and complete for the equational theory of their relational models. Our proof builds on the completeness theorem for Kleene algebra, and on a novel automata construction that makes it possible to extract axiomatic proofs using a Kleene-like algorithm.

BibTeX - Entry

@InProceedings{doumane_et_al:LIPIcs:2018:9556,
  author =	{Amina Doumane and Damien Pous},
  title =	{{Completeness for Identity-free Kleene Lattices}},
  booktitle =	{29th International Conference on Concurrency Theory  (CONCUR 2018)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Sven Schewe and Lijun Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9556},
  URN =		{urn:nbn:de:0030-drops-95564},
  doi =		{10.4230/LIPIcs.CONCUR.2018.18},
  annote =	{Keywords: Kleene algebra, Graph languages, Petri Automata, Kleene theorem}
}

Keywords: Kleene algebra, Graph languages, Petri Automata, Kleene theorem
Collection: 29th International Conference on Concurrency Theory (CONCUR 2018)
Issue Date: 2018
Date of publication: 31.08.2018

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