Analysis of Petri Nets by Ordering Relations in Reduced Unfoldings

This paper suggests a way for Petri Net analysis by checking the ordering relations between places and transitions. The method is based on unfolding the original net into an equivalent acyclic description. We improved on the previously known cutoff criterion for truncating unfoldings [13]. No restrictions are imposed on the class of general PNs. The new criterion significantly reduces the size of an unfolding obtained by a PN. The properties of PNs for analysis can be various: boundedness, safety, persistency etc. A practical example of the suggested approach is given in an application to asynchronous design. Circuit behavior is specified by an interpreted Petri net, called a Signal Transition Graph (STG) which is then analyzed for implementability by an asynchronous hazard-free circuit. The implementability conditions are formulated in such a way that they can be checked by analysis of ordering relations between signal transitions rather than by traversal of states. This allows us to avoid the state explosion problem for highly parallel specifications. The experimental results show that for highly parallel STGs checking their implementability by an unfolding is one to two orders of magnitude less time-consuming than checking it by symbolic BDD traversal of the corresponding State Graph.