Sequential versus concurrent languages of labeled conflict-free Petri nets

For structurally deterministic labeled conflict-free Petri nets (PNs), we show that two PNs have identical sequential languages if and only if their concurrent languages are identical as well, and whether a given labeled conflict-free PN is structurally deterministic or not can be checked in polynomial time. We also investigate a number of language-related problems in supervisory control theory for this class of PNs. As it turns out, the properties of controllability, observability, and normality in the sequential framework coincide with that in the concurrent framework.