On series-parallel pomset languages: rationality, context-freeness and automata

Tobias Kappé (Corresponding author), Paul Brunet, Bas Luttik (Corresponding author), Alexandra Silva, Fabio Zanasi

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs. Like previous Kleene Algebra extensions, developing a correspondence between denotational and operational perspectives is important, both for foundations and for applications. This paper takes an important step towards such a correspondence, by precisely relating bi-Kleene Algebra (BKA), a fragment of CKA, to a novel type of automata called pomset automata (PAs).

We show that PAs can implement the BKA semantics of series-parallel rational expressions, and that a class of PAs can be translated back to these expressions. We also characterise the behaviour of general PAs in terms of context-free pomset grammars; consequently, universality, equivalence and series-parallel rationality of general PAs are undecidable.
Original languageEnglish
Pages (from-to)130-153
Number of pages24
JournalJournal of Logic and Algebraic Programming
Volume103
DOIs
Publication statusPublished - Feb 2019

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