On SeriesParallel Pomset Languages: Rationality, ContextFreeness and Automata
Concurrent Kleene Algebra (CKA) is a formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, an important tool to develop foundations and potential applications is a oneto one correspondence between denotational and operational perspectives. This paper takes an important step towards such a correspondence, by precisely relating BiKleene Algebra (BKA), a relaxed version of CKA, to a novel type of automata called pomset automata. We show that pomset automata can faithfully represent the BKAsemantics of seriesparallel rational expressions, and that a (structurally restricted) class of pomset automata can be translated back to these expressions. Furthermore, we characterise the behavior of unrestricted automata in terms of contextfree pomset grammars, thus yielding strong undecidability results.
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