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Completeness for Identity-free Kleene Lattices

Authors Amina Doumane, Damien Pous

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Author Details

Amina Doumane
  • Univ Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIP, Lyon, France
Damien Pous
  • Univ Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIP, Lyon, France

Funding

This work has been funded by the European Research Council (ERC) under the European Union’s Horizon 2020 programme (CoVeCe, grant agreement No 678157). This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Amina Doumane and Damien Pous. Completeness for Identity-free Kleene Lattices. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CONCUR.2018.18

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Regular languages
Keywords
  • Kleene algebra
  • Graph languages
  • Petri Automata
  • Kleene theorem

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