### Abstract

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.

Original language | English |
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Title of host publication | 28th International Conference on Concurrency Theory (CONCUR 2017) |

Editors | Roland Meyer, Uwe Nestmann |

Place of Publication | Dagstuhl |

Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |

Pages | 1-16 |

Number of pages | 16 |

ISBN (Electronic) | 9783959770484 |

DOIs | |

Publication status | Published - 1 Aug 2017 |

Event | 28th International Conference on Concurrency Theory, CONCUR 2017 - Berlin, Germany Duration: 5 Sep 2017 → 8 Sep 2017 |

### Publication series

Name | Leibniz International Proceedings in Informatics (LIPIcs) |
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Publisher | Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik |

Volume | 85 |

### Conference

Conference | 28th International Conference on Concurrency Theory, CONCUR 2017 |
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Country | Germany |

City | Berlin |

Period | 5/09/17 → 8/09/17 |

### Keywords

- Automata
- Brzozowski derivatives
- Concurrency
- Kleene theorem
- Pomsets
- Series-rational expressions

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## Cite this

Kappé, T., Brunet, P., Luttik, B., Silva, A., & Zanasi, F. (2017). Brzozowski goes concurrent: A Kleene Theorem for pomset languages. In R. Meyer, & U. Nestmann (Eds.),

*28th International Conference on Concurrency Theory (CONCUR 2017)*(pp. 1-16). [25] (Leibniz International Proceedings in Informatics (LIPIcs); Vol. 85). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2017.25