Verification of Asynchronous Programs with Nested Locks

In this paper, we consider asynchronous programs consisting of multiple threads running in parallel. Each of the thread is equipped with a multi-set. The threads can create tasks and post them onto multi-sets of other threads or read a task from their own. In addition, they can synchronise through a finite set of locks. In this paper, we show that the reachability problem of such class of asynchronous programs is undecidable even under the nested locking policy. We then show that the reachability problem becomes decidable (Exp-space-complete) when the locks are not allowed to be held across tasks. Finally, we show that the problem is NP-complete when in addition to previous restrictions, threads always read tasks from the same state.