Saturation Enhanced with Conditional Locality: Application to Petri Nets

Abstract

The saturation algorithm for symbolic state space generation has proved to be an efficient way to tackle the state space explosion problem in the verification of concurrent, asynchronous systems. Since its original publication in 2001, several variants and extensions have been introduced. The reason for altering the algorithm in these variants is often specific to how it handles transitions. Saturation heavily relies on the notion of locality: transitions tend to affect only some of the state variables. The saturation effect, however, can be achieved and even enhanced with a weaker notion of locality, which we call conditional locality. In this paper, we define a generalized version of the saturation algorithm (GSA) for multi-valued decision diagrams that works with conditional locality and show that it enables the direct usage of transition relations that previously required a specialized algorithm such as variants of constrained saturation. Focusing on Petri nets, we also empirically demonstrate on models of the Model Checking Contest that the GSA often outperforms the original saturation algorithm whenever conditional locality can be exploited and has virtually no overhead for other models.