On Decidability of Concurrent Kleene Algebra
CONCUR
in Berlin,
September 2017
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.
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Related papers | ||
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Equivalence checking for weak bi-Kleene algebra
(in LMCS 2021)
with Tobias Kappé, Alexandra Silva, Bas Luttik and Fabio Zanasi. |
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Partially Observable Concurrent Kleene Algebra
(in CONCUR 2020)
with Jana Wagemaker, Simon Docherty, Jurriaan Rot, Tobias Kappé and Alexandra Silva. |
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Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
(in FoSSaCS 2020)
with Tobias Kappé, Alexandra Silva, Fabio Zanasi and Jana Wagemaker. |
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Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra
(in FSCD 2020)
with David Pym. |
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On Series-Parallel Pomset Languages: Rationality, Context-Freeness and Automata
(in JLAMP 2019)
with Tobias Kappé, Alexandra Silva, Bas Luttik and Fabio Zanasi. |
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Kleene Algebra with Observations
(in CONCUR 2019)
with Tobias Kappé, Alexandra Silva, Fabio Zanasi, Jurriaan Rot and Jana Wagemaker. |
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Concurrent Kleene Algebra: Free Model and Completeness
(in ESOP 2018)
with Tobias Kappé, Alexandra Silva and Fabio Zanasi. |
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Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages
(in CONCUR 2017)
with Tobias Kappé, Alexandra Silva, Bas Luttik and Fabio Zanasi. |
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On Decidability of Concurrent Kleene Algebra
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with Damien Pous and Georg Struth. |
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