Concurrent Implementation of Asynchronous Transition Systems

The synthesis problem is to decide for a deterministic transition system whether a Petri net with an isomorphic reachability graph exists and in case to find such a net (which must have the arc-labels of the transition system as transitions). In this paper, we weaken isomorphism to some form of bisimilarity that also takes concurrency into account and we consider safe nets that may have additional internal transitions. To speak of concurrency, the transition system is enriched by an independence relation to an asynchronous transition system. For an arbitrary asynchronous transition system, we construct an ST-bisimilar net. We show how to decide effectively whether there exists a bisimilar net without internal transitions, in which case we can also find a history-preserving bisimilar net without internal transitions. Finally, we present a construction that inserts a new internal event into an asynchronous transition system such that the result is history-preserving bisimilar; this construction can help to find a history-preserving bisimilar net (with internal transitions).