Topological reverse mirroring: a new efficient knowledge-based methodology of reachability analysis for Petri nets

Abstract

‘Topological reverse mirroring’ (TRM) is a new knowledge-based methodology for more efficiently analysing reachability to derive the closed-form formulas (CFF) of the number of Control-Related states for PNs. According to variant k-th order systems, TRM is constructed by proving that both Gen-Right(k, gen) and Gen_Left(k, k−gen) are the topological reverse nets of Gen-Left(k, gen) such that there is a reversible one-to-one mapping (Mirroring) between these two systems. Thus Gen-Right(k, gen) and Gen-Left(k, k−gen) have same CFF which can be immediately derived by replacing the parameter ‘gen’ by ‘k−gen’ in validated CFF for Gen-Left(k, gen). The shown applications of TRM include the reachability analysing for systems with non-sharing sub-net; Deficient tokens; multi-non-sharing/multi-tokens resources; and multi-processes. This paper reports the core methodology to accelerate furthering emerging system-control applications for more complicated PNs based on the real-time information derived by their CFF.