This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions.To provide a solution for the notorious problem, it is essential to present an here effective characterization in such a way that deadlock control and synthesis are technically and methodologically possible.To this end, we introduce the notion of dangerous implicit vectors (DIVs), which implicitly threaten the system deadlock-freedom.The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs).An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system.
Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions for identifying the existence g5210t-p90 of blocking markings in an LPN.Finally, an algorithm is developed to construct an observed graph that is a compendious presentation of the reachability graph of a net system, with respect to the existence of dead reaches.At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented.