Coverability graphs for a class of synchronously executed unbounded petri net

Abstract

Synchronous (or concurrent) transition firing rules for Petri nets are useful in modeling computations on real-time systems with multiple processors. A synchronous firing rule is one in which more than one transition may be fired to effect a single state change, allowing the physically concurrent operation of multiple hardware processors to be represented in the state sequence without including intermediate states that have no meaningful physical interpretation. A simple counterexample illustrates that the standard method of generating a Petri net coverability graph is insufficient to represent the reachability set of a Petri net operating under a synchronous firing rule. We describe a variant of one widely used concurrent execution rule (that of firing maximal subsets) in which the simultaneous firing of conflicting transitions is prohibited. An algorithm is then given for constructing the coverability graph of a net executed under this synchronous firing rule. The ω insertion criteria in the algorithm are shown to be valid for any net on which the algorithm terminates; the set of nets on which the algorithm terminates is then shown to properly include the conflict free class.