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

Basis marking representation of Petri net reachability spaces and its application to the reachability problem

In this paper a compact representation of the reachability graph of a Petri net is proposed. The transition set of a Petri net is partitioned into the subsets of explicit and implicit transitions, in such a way that the subnet induced by implicit transitions does not contain directed cycles. The firing of implicit transitions can be abstracted so that the reachability set of the net can be completely characterized by a subset of reachable markings called basis makings. We show that to determine a max-cardinality-T_I basis partition is an NPhard problem, but a max-set-T_I basis partition can be determined in polynomial time. The generalized version of the marking reachability problem in a Petri net can be solved by a practically efficient algorithm based on the basis reachability graph. Finally this approach is further extended to unbounded nets

Petri nets for modelling metabolic pathways: a survey

In the last 15 years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net

Nested-unit Petri nets

International audiencePetri nets can express concurrency and nondeterminism but neither locality nor hierarchy. This article presents an extension of Petri nets, in which places can be grouped into so-called "units" expressing sequential components. Units can be recursively nested to reflect both the concurrent and hierarchical nature of complex systems. This model called NUPN (Nested-Unit Petri Nets) was originally developed for translating process calculi to Petri nets, but later found also useful beyond this setting. It allows significant savings in the memory representation of markings for both explicit-state and symbolic verification. Thirteen software tools already implement the NUPN model, which has also been adopted for the benchmarks of the Model Checking Contest (MCC) and the parallel problems of the Rigorous Examination of Reactive Systems (RERS) challenges

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 Reviewe