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, for both foundations
and 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, 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 behavior of general PAs in terms of context-free pomset grammars;
consequently, universality, equivalence and series-parallel rationality of
general PAs are undecidable.Comment: Accepted manuscrip
