On the Synchronization of Semi-Traces

The synchronization of two or more semi-traces describes the possible evaluation of a concurrent system, which consists of two or more concurrent subsystems in a modular way, where communication between the subsystems restricts the order of the actions. In this paper we give criteria, which tell us for given semi-traces in given semicommutation systems, whether they are synchronizable and whether the synchronization is again a semi-trace; and criteria, which tell us for given semi-commutation systems, whether all semi-traces have this property. We prove that deciding these criteria is NLOGSPACE-complete for given semi-traces. The same holds for the synchronizability of all semitraces for given semi-commutation systems. On the other hand the question, whether for given semi-commutation systems the synchronization of synchronizable semi-traces is a semi-trace is co-NP-complete. Furthermore we give a co-NP-complete condition for being able to decide synchronizability locally in TC.