Labelled domains and automata with concurrency

AbstractWe investigate an operational model of concurrent systems, called automata with concurrency relations. These are labelled transition systems A in which the event set is endowed with a collection of binary concurrency relations which indicate when two events, in a particular state of the automaton, commute. This model generalizes asynchronous transition systems, and as in trace theory we obtain, through a permutation equivalence for computation sequences of A, an induced domain (D(A), ⩽). Here, we construct a categorical equivalence between a large category of (“cancellative”) automata with concurrency relations and the associated domains. We show that each cancellative automaton can be reduced to a minimal cancellative automaton generating, up to isomorphism, the same domain. Furthermore, when fixing the event set, this minimal automaton is unique