Linear Programming Deadlock Checking Using Partial Order Dependencies

Model checking based on the causal partial order semantics of Petri nets is an approach widely applied to cope with the state space explosion problem. One of the ways to exploit such a semantics is to consider (finite prefixes of) net unfoldings — themselves a class of acyclic Petri nets — which contain enough information, albeit implicit, to reason about the reachable markings of the original Petri nets. In [15], a verification technique for net unfoldings was proposed in which deadlock detection was reduced to a mixed integer linear programming problem. In this paper, we present a further development of this approach. We adopt Contejean-Devie’s algorithm for solving systems of linear constraints over the natural numbers domain and refine it, by taking advantage of the specific properties of systems of linear constraints to be solved. The essence of the proposed modifications is to transfer the information about causality and conflicts between the events involved in an unfolding, into a relationship between the corresponding integer variables in the system of linear constraints. Experimental results demonstrate that the new technique achieves significant speedups.