Delay-dependent partial order reduction technique for real time systems

Almost all partial order reduction techniques proposed for time Petri nets (TPNs in short) are based on the notion of Partially Ordered Sets. The idea is to explore simultaneously, by relaxing some firing order constraints of persistent transitions (An enabled transition is persistent, if it cannot be disabled until its firing.), several equivalent sequences, while computing the convex hull of the abstract states reached by these equivalent sequences. However, unlike timed automata, in the TPN state space abstractions, the union of the abstract states reached by different interleavings of the same set of non conflicting transitions is not necessarily identical to their convex hull. Moreover, the convex hull over-approximation preserves neither the boundedness nor the reachability properties of the TPN. In this context, the main challenge is to establish sufficient conditions over transitions that ensure, in addition to their persistency, identity between the union and the convex hull of the abstract states reachable by their different interleavings. This paper shows how to weaken the sufficient conditions proposed in the literature, by taking into better account the structure, the marking, the static and the dynamic time parameters of the TPN.