We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability property on a reduced version of this net. This method relies on a new state space abstraction based on systems of linear equations, called polyhedral abstraction. We prove the correctness of this method using a new notion of equivalence between nets. We provide a complete framework to define and check the correctness of equivalence judgements; prove that this relation is a congruence; and give examples of basic equivalence relations that derive from structural reductions. 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 in the Model Checking Contest. Our experimental results show that our approach works well, even when we only have a moderate amount of reductions
翻译:我们与基于SMT的模型校验器共同界定了利用净削减和基于SMT的模型校验器的新方法。我们的方法是将某些Petri网的可达性问题转化为核查该网减少版本上的最新可达性财产的核查。这个方法依靠基于线性方程系统的新状态空间抽象,称为多元抽象抽象。我们用一种新的网对等概念来证明这种方法的正确性。我们提供了一个完整的框架来界定和检查对等性判断的正确性;证明这一关系是一致的;并举例说明结构性削减产生的基本等同关系。我们的方法是在一个称为SMPT的工具中实施的,它提供了两个主要程序:完善的示范检查(BMC)和产权直接可达性(PDR)。每一个程序都经过调整,以便使用削减和任意的Petri网。我们用大量查询来测试SMPT。我们的实验结果表明,即使我们只有适度的削减数量,我们的方法也是有效的。