Computing Structural Properties of Symmetric Nets

Abstract

Structural properties of Petri Nets (PN) have an important role in the process of model validation and analysis. When dealing with high level Petri nets (HLPN) structural analysis still poses many problems and often tools go through the unfolding of the HLPN model and apply PN structural analysis techniques to the unfolded model: with this approach the symmetries present in the models are completely ignored and cannot be exploited. Structural properties of HLPN can be defined as relations among node instances using symbolic and parametric expressions; the computation of such expressions from the model structure and annotations requires the development of a specific calculus, as the one proposed in the literature for Symmetric Nets (SN). When dealing with Stochastic SN (SSN), comprising stochastic timed transitions and immediate transitions, structural analysis becomes a fundamental step in net-level definition of probabilistic parameters. Moreover some structural relations allow to automatize the derivation of symbolic Ordinary Differential Equations for the solution of SSN models with huge state space. The goal of the present paper is to summarize the language defined to express SNs' structural relations, to complete the formalization of some interesting structural properties as expressions of the calculus, and to provide examples of their use. The algorithms required to support the calculus for symbolic structural relations computation have been recently completed and implemented in a tool called SNexpression.

A structural approach to graph transformation based on symmetric Petri nets

“…SN show an acceptable trade-off between expressivity and analysis capability. Efficient algorithms are available for both state-space based [23] and structural [24,25] analysis of SN. Many of these are integrated in GreatSPN [22], a graphical editor for SN, whereas the most recent advances on structural analysis are implemented in SNexpression [26] (www.di.unito.it/~depierro/SNex), a kind of computer-algebra system.…”

“…The associated quotient graph (called Symbolic Reachability Graph) [23], which directly comes from a symbolic graph encoding, naturally abstracts from graph isomorphism. Above all, some recent advances in SN symbolic structural analysis [24,25], implemented in SNexpression tool [26] (www.di.unito.it/~depierro/SNex), allow you to efficiently validate rules and verify general properties of a GTS, such as conflicts, mutual-exclusion, semi-flows.…”

An Operational Semantics of Graph Transformation Systems Using Symmetric Nets

“…This formalism is thus convenient from the point of view of model representation as well as from that of its analysis. Efficient methods have been proposed to perform SN state-space based analysis [7], or structural analysis [4], [3]. Many of these algorithms have been implemented in GreatSPN [1], whereas the most recent developments on structural analysis have been implemented in SNexpression (www.di.unito.it/~depierro/SNex).…”

“…We have to establish some conditions ensuring that a rewriting rule is well-defined, that is, any instance of the rule (transition) rewrites a (simple) directed graph into another one. By exploiting the calculus for SN introduced in [3], [4], it is possible to characterize these rules as structural conditions on the arc functions annotating the corresponding transition, that may be checked in a fully symbolic and automated way, e.g., by using the SNexpression (www.di.unito.it/~depierro/SNex) toolset.…”

“…Some practical exploitations of the proposed operational semantics are discussed. In particular, a recently developed structural calculus for SN is used to validate graph rewriting rules in a symbolic way.An Operational Semantics of GTS the GreatSPN package [1]; an operational interleaving semantics for GTS is provided in a natural way building the state-transition system of a SN; a compact state-transition system -called symbolic reachability graph [7], in which states (markings) representing isomorphic graphs are folded, can be directly derived once an initial symbolic graph encoding is set; some recent advances in SN (symbolic) structural analysis [4], [3], implemented in the SNExpression tool (www.di.unito.it/~depierro/SNex) may be exploited to check some conditions ensuring rule well-definiteness, validate rules, and verify their potential concurrency; in particular, a fully automated calculus of symbolic structural relations in SN models may be profitably used. All these concepts are instantiated on a few, though significant, examples of graph rewriting rules, and a simple GTS.…”