From PNML to counter systems for accelerating Petri Nets with FAST

We use the tool FAST to check parameterized safety properties on Petri nets with a large or infinite state space. Although this tool is not dedicated to Petri nets, it can be used for these as place/transition nets (and some of their extensions) are subcases of FASTinput model. The originality of the tool lies in the use of acceleration techniques in order to compute the exact reachability set for infinite systems. In this paper, we present the automatic transformation of Petri nets written in PNML (Petri Net Markup Language) into counter systems. Then, FAST provides a simple but very powerful language to express complex properties and check these

Proving a Petri net model-checker implementation

Petri nets are a widely used tool in verification through model-checking. In this approach, a Petri Net model of the system of interest is produced and its reachable states are computed, searching for erroneous executions. Compilation of such a Petri net model is one way to accelerate its verification. It consists in generating code to explore the reachable states of the considered Petri net, which avoids the use of a fixed exploration tool involving an "interpretation" of the Petri net structure. In this paper, we show how to compile Petri nets targeting the LLVM language (a high-level assembly language) and formally prove the correct-ness of the produced code. To this aim, we define a structural operational semantics for the fragment of LLVM we use. The acceleration obtained from the presented compilation techniques has been evaluated in [6]

Flatness and Complexity of Immediate Observation Petri Nets

In a previous paper we introduced immediate observation (IO) Petri nets, a class of interest in the study of population protocols and enzymatic chemical networks. In the first part of this paper we show that IO nets are globally flat, and so their safety properties can be checked by efficient symbolic model checking tools using acceleration techniques, like FAST. In the second part we study Branching IO nets (BIO nets), whose transitions can create tokens. BIO nets extend both IO nets and communication-free nets, also called BPP nets, a widely studied class. We show that, while BIO nets are no longer globally flat, and their sets of reachable markings may be non-semilinear, they are still locally flat. As a consequence, the coverability and reachability problem for BIO nets, and even a certain set-parameterized version of them, are in PSPACE. This makes BIO nets the first natural net class with non-semilinear reachability relation for which the reachability problem is provably simpler than for general Petri nets

From PNML to counter systems for accelerating Petri Nets with FAST

We use the tool FAST to check parameterized safety properties on Petri nets with a large or infinite state space. Although this tool is not dedicated to Petri nets, it can be used for these as place/transition nets (and some of their extensions) are subcases of FASTinput model. The originality of the tool lies in the use of acceleration techniques in order to compute the exact reachability set for infinite systems. In this paper, we present the automatic transformation of Petri nets written in PNML (Petri Net Markup Language) into counter systems. Then, FAST provides a simple but very powerful language to express complex properties and check these

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Minimal Coverability Set for Petri Nets: Karp and Miller Algorithm with Pruning

This paper presents the Monotone-Pruning algorithm (MP) for computing the minimal coverability set of Petri nets. The original Karp and Miller algorithm (K&M) unfolds the reachability graph of a Petri net and uses acceleration on branches to ensure termination. The MP algorithm improves the K&M algorithm by adding pruning between branches of the K&M tree. This idea was first introduced in the Minimal Coverability Tree algorithm (MCT), however it was recently shown to be incomplete. The MP algorithm can be viewed as the MCT algorithm with a slightly more aggressive pruning strategy which ensures completeness. Experimental results show that this algorithm is a strong improvement over the K&M algorithm as it dramatically reduces the exploration tree