Source Sets: A Foundation for Optimal Dynamic Partial Order Reduction

Stateless model checking is a powerful method for program verification that, however, suffers from an exponential growth in the number of explored executions. A successful technique for reducing this number, while still maintaining complete coverage, is Dynamic Partial Order Reduction (DPOR), an algorithm originally introduced by Flanagan and Godefroid in 2005 and since then not only used as a point of reference but also extended by various researchers. In this article, we present a new DPOR algorithm, which is the first to be provably optimal in that it always explores the minimal number of executions. It is based on a novel class of sets, called source sets, that replace the role of persistent sets in previous algorithms. We begin by showing how to modify the original DPOR algorithm to work with source sets, resulting in an efficient and simple-to-implement algorithm, called source-DPOR. Subsequently, we enhance this algorithm with a novel mechanism, called wakeup trees, that allows the resulting algorithm, called optimal-DPOR, to achieve optimality. Both algorithms are then extended to computational models where processes may disable each other, for example, via locks. Finally, we discuss tradeoffs of the source-and optimal-DPOR algorithm and present programs that illustrate significant time and space performance differences between them. We have implemented both algorithms in a publicly available stateless model checking tool for Erlang programs, while the source-DPOR algorithm is at the core of a publicly available stateless model checking tool for C/pthread programs running on machines with relaxed memory models. Experiments show that source sets significantly increase the performance of stateless model checking compared to using the original DPOR algorithm and that wakeup trees incur only a small overhead in both time and space in practice.