On the Combination of Polyhedral Abstraction and SMT-Based Model Checking for Petri Nets

Abstract

We define a method for taking advantage of net reductions in combination with a SMT-based model checker. We prove the correctness of this method using a new notion of equivalence between nets that we call polyhedral abstraction. Our approach has been implemented in a tool, named SMPT, that provides two main procedures: Bounded Model Checking (BMC) and Property Directed Reachability (PDR). Each procedure has been adapted in order to use reductions and to work with arbitrary Petri nets. We tested SMPT on a large collection of queries used during the 2020 edition of the Model Checking Contest. Our experimental results show that our approach works well, even when we only have a moderate amount of reductions.

Accelerating the Computation of Dead and Concurrent Places Using Reductions

“…While there are many examples of the benefits of structural 1 arXiv:2106.12813v1 [cs.LO] 24 Jun 2021 reductions when model checking Petri nets, the use of an equation system (E) for tracing back the effect of reductions is new, and we are hopeful that this approach can be applied to other problems. For example, we proved recently [1] that this approach also works well when combined with SMT.…”

“…Polyhedral Abstraction. We recently defined a notion of polyhedral abstraction based on our previous work applying structural reductions to model counting [1,5]. We only need a simplified version of this notion here, which entails an equivalence between the state space of two nets, (N 1 , m 1 ) and (N 2 , m 2 ), "up-to" a system E of linear equations.…”

“…In practice, we start from an initial net, (N 1 , m 1 ), and derive (N 2 , m 2 ) and E using a combination of several structural reduction rules. You can find a precise description of our set of rules in [5] and a proof that the result of these reductions always leads to a valid E-equivalence in [1]. In most cases, the system of linear equations obtained using this process exhibits a graph-like structure.…”

“…We recently became interested in this problem because we see it as a good testbed for a new model checking technique that we are actively developing [1,4,5]. It is an abstraction technique, based on the use of structural reductions [3], that we successfully implemented into a symbolic model checker called Tedd.…”

Kong: A Tool to Squash Concurrent Places

“…The correctness of our tool relies on two main theoretical notions. First, a new state space abstraction method, that we called polyhedral abstraction in [1], which involves a combination of structural reductions and linear arithmetic constraints between the marking of places. Second, a new data structure, called Token Flow Graph (TFG) in [2], that can be used to compute properties based on a polyhedral abstraction.…”