Automatic Symmetry Detection in Well-Formed Nets

Abstract

Abstract. Formal verification of complex systems using high-level Petri Nets faces the so-called state-space explosion problem. In the context of Petri nets generated from a higher level specification, this problem is particularly acute due to the inherent size of the considered models. A solution is to perform a symbolic analysis of the reachability graph, which exploits the symmetry of a model. Well-Formed Nets (WN) are a class of high-level Petri nets, developed specifically to allow automatic construction of a symbolic reachability graph (SRG), that represents equivalence classes of states. This relies on the definition by the modeler of the symmetries of the model, through the definition of "static sub-classes". Since a model is self-contained, these (a)symmetries are actually defined by the model itself. This paper presents an algorithm capable of automatically extracting the symmetries inherent to a model, thus allowing its symbolic study by translating it to WN. The computation starts from the assumption that the model is entirely symmetric, then examines each component of a net to deduce the symmetry break it induces. This translation is transparent to the end-user, and is implemented as a service for the AMI-Net package. It is particularly adapted to models containing large value domains, yielding combinatorial gain in the size of the reachability graph.

On the Formal Verification of Middleware Behavioral Properties

“…We also take into account the property to be checked, allowing further reductions by abstracting away behaviors that are not observed by the property, using dynamically adapted on-the-fly algorithms. This section superficially explains how the tools work (complete descriptions of the algorithms can be found in [25,2]). Moreover, these techniques may be used through a simple interface, that requires no knowledge of these internals.…”

“…Recent works have automated the analysis of the symmetries allowed by a system [25], and of the symmetries allowed by a property [2], allowing full LTL model-checking while efficiently fighting the well-known combinatorial statespace explosion problem. As we show in sections 5.2 and 6.1, the use of these symmetry-based reductions allows us to verify the properties of our system, while plain state-space generation is unfeasible with classic techniques.…”

“…To analyze the symmetries of a system, our algorithm [25] examines each action (transition) of the system to find which elements (if any) it distinguishes, and concludes that any element distinguished by at least one action should be distinguished in R. The result of this symmetry analysis is an equivalence relation R that lists for each data type the symmetric values with respect to the language of the actions of the system. This automatic computation ensures that any elements considered equivalent under R are not distinguished by any action of the system.…”

“…Our models were created using CPN-AMI [15], a Petri net CASE environment that integrates structural analysis tools and model checkers. We then analyse data type symmetries [25] and compute the reduced state space using the Great-SPN [7] tool-suite and extensions for SSP. Finally for LTL model-checking, we used the model checking library Spot [16], in conjunction with GreatSPN.…”

Modeling and Analyzing Wireless Sensor Networks with VeriSensor: An Integrated Workflow

“…All constraints are combined to produce a minimal set of values for each domain. Such techniques are derived from automatic symmetry detection [42] or symbolic trajectory evaluation [1]. The complexity of these techniques is low, since it relies on the size of the specification instead of the size of the state space.…”