Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages
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.
Cite
@article{arxiv.1704.07199,
title = {Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages},
author = {Tobias Kappé and Paul Brunet and Bas Luttik and Alexandra Silva and Fabio Zanasi},
journal= {arXiv preprint arXiv:1704.07199},
year = {2023}
}
Comments
Version 2 incorporates changes prompted by comments of the anonymous referees at CONCUR. Besides minor corrections, this includes additions to the introduction and the discussion section, as well as a proof of Lemma 2.5. Version 3 corrects the accent on the first author's surname in the metadata