Structural methods to improve the symbolic analysis of Petri nets

Symbolic techniques based on BDDs (Binary Decision Diagrams) have emerged as an efficient strategy for the analysis of Petri nets. The existing techniques for the symbolic encoding of each marking use a fixed set of variables per place, leading to encoding schemes with very low density. This drawback has been previously mitigated by using Zero-Suppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. Structural Petri net theory provides P-invariants that help to derive more efficient encoding schemes for the BDD representations of markings. P-invariants also provide a mechanism to identify conservative upper bounds for the reachable markings. The unreachable markings determined by the upper bound can be used to alleviate both the calculation of the exact reachability set and the scrutiny of properties. Such approach allows to drastically decrease the number of variables for marking encoding and reduce memory and CPU requirements significantly.Peer ReviewedPostprint (author's final draft

Proving nonreachability by modulo-invariants

AbstractWe introduce modulo-invariants of Petri nets which are closely related to classical place-invariants but operate in residue classes modulo k instead of natural or rational numbers. Whereas place-invariants prove the nonreachability of a marking if and only if the corresponding marking equation has no solution in Q, a marking can be proved nonreachable by modulo-invariants if and only if the marking equation has no solution in Z. We show how to derive from each net a finite set of invariants — containing place-invariants and modulo-invariants — such that if any invariant proves the nonreachability of a marking, then some invariant of this set proves that the marking is not reachable