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On Decidability of Concurrent Kleene Algebra

Authors Paul Brunet, Damien Pous, Georg Struth

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Paul Brunet
Damien Pous
Georg Struth

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Paul Brunet, Damien Pous, and Georg Struth. On Decidability of Concurrent Kleene Algebra. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CONCUR.2017.28

Abstract

Concurrent Kleene algebras support equational reasoning about
computing systems with concurrent behaviours. Their natural
semantics is given by series(-parallel) rational pomset languages, a
standard true concurrency semantics, which is often associated with
processes of Petri nets. We use constructions on Petri nets to
provide two decision procedures for such pomset languages motivated
by the equational and the refinement theory of concurrent Kleene
algebra. The contribution to the first problem lies in a much
simpler algorithm and an EXPSPACE complexity bound. Decidability
of the second, more interesting problem is new and, in fact,
EXPSPACE-complete.

Subject Classification

Keywords
  • Concurrent Kleene algebra
  • series-parallel pomsets
  • Petri nets

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References

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