Property Directed Reachability for Generalized Petri Nets

Abstract

We propose a semi-decision procedure for checking generalized reachability properties, on generalized Petri nets, that is based on the Property Directed Reachability (PDR) method. We actually define three different versions, that vary depending on the method used for abstracting possible witnesses, and that are able to handle problems of increasing difficulty. We have implemented our methods in a model-checker called SMPT and give empirical evidences that our approach can handle problems that are difficult or impossible to check with current state of the art tools.

SMPT: A Testbed for Reachability Methods in Generalized Petri Nets

“…As can be expected, we say that F is reachable in (N, m 0 ) if there is m reachable such that m |= F . See [2,3,6] for more details. We support two categories of queries: EF F , which is true only if F is reachable; and AG F , which is true when F is an invariant, with the classic relationship that AG F ≡ ¬ (EF ¬F ).…”

“…This method can return a verdict certificate. We provide three different methods of increasing complexity [6] (one for coverability and two for general reachability).…”

“…Our repository includes a script to simplify the installation of the tool and all its dependencies. It is also possible to find disk images with a running installation in the MCC website and in artifacts archived on Zenodo [4,5]. As usual, option --help returns an abridged description of all the available options.…”

“…This explains why it includes many "reference" implementations of fundamental reachability algorithms, tailored for Petri nets, such as Bounded Model Checking (BMC) [17,22,8] or k-induction [31]. It also includes new verification methods, such as adaptations of Property Directed Reachability (PDR) [15,16] for Petri nets [6]. One of our goal is to efficiently compare different algorithms, on a level playing field, with the the ability to switch on or off optimizations.…”