Improving the State Space Computation of the Time Stream Petri Nets Model

Abstract

An enumerative technique is presented allowing the reachability analysis of weakly synchronous systems modeled using time stream Petri net (TSPN). In a TSPN, time constraints are associated with incoming arcs, whereas synchronization rules are associated with transitions, thus allowing the violation of time constraints. We propose an approach to contract the TSPN state space by building its state class graph. Each class therein is a pair (M, D), where M is a marking and D is a system that can be encoded in a difference bound matrix, as long as no arc's time constraint violation is reported. Hence, each reachable class is computed by applying an optimal algorithm in a square complexity time. For this effect, efficient conditions for the consistency, firing and equivalence tests are provided to ensure a finite graph construction when the model is bounded. Finally, in order to validate our approach, experimental results are reported.