Fault Detection and Initial State Verification by Linear Programming for a Class of Petri Nets

A problem encountered in using Petri nets to model systems is analyzing a given marking of the Petri net for such properties as liveness and safeness. For a restricted class of Petri nets, specifically live safe marked graphs (LSMGs) and live safe free choice (LSFC) nets, these properties can be analyzed by determining if the marking, m, of the modeled system is within the set of live safe markings, denoted by M. Since M is a forward invariant, during normal net operation deviation from M indicates a fault. This paper presents the conditions for a marking to be in M, and an efficient algorithm, using linear programming, to determine when these conditions are met.