2026-07-24T00:02:56Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7791 2024-03-06T10:41:09Z ddc:004 open_access

Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages Kappé, Tobias Brunet, Paul Luttik, Bas Silva, Alexandra Zanasi, Fabio Kleene theorem Series-rational expressions Automata Brzozowski derivatives Concurrency Pomsets Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this paper makes an important step towards an answer. We present a new automaton model and a Kleene-like theorem that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tobias Kappé and Paul Brunet and Bas Luttik and Alexandra Silva and Fabio Zanasi 2017 Is Part Of LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2017.25 urn:nbn:de:0030-drops-77913 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.25 eng https://creativecommons.org/licenses/by/3.0/legalcode