Integer Linear Programming and the Analysis of Some Petri Net Problems

A class of Petri nets (called type \cal L Petri nets in this paper) whose reachability sets can be characterized by integer linear programming is defined. Such Petri nets include the classes of conflict-free , normal , BPP , trap-circuit , and extendedtrap-circuit Petri nets, which have been extensively studied in the literature. We demonstrate that being of type \cal L is invariant with respect to a number of Petri net operations, using which Petri nets can be pieced together to form larger ones. We also show in this paper that for type \cal L Petri nets, the model checking problem for a number of temporal logics is reducible to the integer linear programming problem, yielding an NP upper bound for the model checking problem. Our work supplements some of the previous results concerning model checking for Petri nets.