SAT-Based Verification of Safe Petri Nets

Abstract

Abstract.Bounded model checking has received recent attention as an efficient verification method. The basic idea behind this new method is to reduce the model checking problem to the propositional satisfiability decision problem or SAT. However, this method has rarely been applied to Petri nets, because the ordinary encoding would yield a large formula due to the concurrent and asynchronous nature of Petri nets. In this paper, we propose a new SAT-based verification method for safe Petri nets. This method can reduce verification time by representing the behavior by very succinct formulas. Through an experiment using a suite of Petri nets, we show the effectiveness of the proposed method.

Bounded Reachability Checking of Asynchronous Systems Using Decision Diagrams

“…In our experiments, SAT-S performs at least as well as the analogous approach using process semantics [17] (this is also confirmed by the results in Heljanko and Junttila's recent tutorial [18]), therefore we report only the former in Table 1. With Corbett's benchmarks, we show different bounds for SAT-C than those reported in [25]; this is due to using a different initial state, the same as the one considered in [18]. For SAT-I and SAT-C both the encoding time and the bczchaff circuit SAT-solver runtime are reported in Table 1.…”

“…For our symbolic algorithms, this check simply requires us to remove the set of states enabling α, i.e., Img −1 ( S, D α ), for each event α, from the final bounded state space. We compare the performance of several decision-diagram-based methods and the SAT-based methods of Heljanko et al [18,19] and Ogata et al [25].…”

“…3) -SAT-S (circuit SAT-based method with step semantics [19]) -SAT-C (CNF SAT-based method with forward chaining [25]) Or compute a superset of the states S B within distance B: -EDD-Approx /EVBDD-Approx (Bounded Saturation: TruncateApprox ) Or "exact" methods that limit their search to exactly S B : -SAT-I (circuit SAT-based method with interleaving semantics [19]) -EDD-Exact /ADD-Exact (Bounded Saturation: TruncateExact). For each approximate method, we report the smallest bound B at which either a deadlock is found or the runtime exceeds 10 minutes.…”

“…Bounded model checking is an incomplete verification technique unless the bound exceeds the state space diameter. However, as many faults involve relatively short counterexamples in practice, the technique has proved itself an efficient debugging aid, and bounded model checkers are now used to verify digital circuits [12], Petri nets [17,25], and software [20,26]. Several studies…”

“…We evaluate Bounded Saturation against two SATbased approaches for bounded reachability checking proposed by Heljanko [17] and Ogata, Tsuchiya, and Kikuno [25], both aimed at finding deadlocks in asynchronous systems specified by Petri nets. We implemented our algorithm in S m A r T [6], and ran it on the suite of examples used in both [17] and [25], first proposed by Corbett in [15], and on two models from the S m A r T release. The static variable ordering used in our algorithm was computed via a heuristic [27].…”