Synchronisation- and Reversal-Bounded Analysis of Multithreaded Programs with Counters

Matthew Hague, Anthony Widjaja Lin

Abstract: We study a class of concurrent pushdown systems communicating by both global synchronisations and reversal-bounded counters, providing a natural model for multithreaded programs with procedure calls and numeric data types. We show that the synchronisation-bounded reachability problem can be efficiently reduced to the satisfaction of an existential Presburger formula. Hence, the problem is NP-complete and can be tackled with efficient SMT solvers such as Z3. In addition, we present optimisations to make our reduction practical, e.g., heuristics for removing or merging transitions in our models. We provide optimised algorithms and a prototypical implementation of our results and perform preliminary experiments on examples derived from real-world problems.