Bounded Context-Switching and Reentrant Locking

Reentrant locking is a recursive locking mechanism which allows a thread in a multi-threaded program to acquire the reentrant lock multiple times. The thread must release this lock an equal number of times before another thread can acquire this lock. We consider the control state reachability problem for recursive multi-threaded programs synchronizing via a finite number of reentrant locks. Such programs can be abstracted as multi-pushdown systems with a finite number of counters. The pushdown stacks model the call stacks of the threads and the counters model the reentrant locks. The control state reachability problem is already undecidable for non-reentrant locks. As a consequence, for non-reentrant locks, under-approximation techniques which restrict the search space have gained traction. One popular technique is to limit the number of context switches. Our main result is that the problem of checking whether a control state is reachable within a bounded number of context switches is decidable for recursive multi-threaded programs synchronizing via a finite number of reentrant locks if we restrict the lock-usage to contextual locking: a release of an instance of reentrant lock can only occur if the instance was acquired before in the same procedure and each instance of a reentrant lock acquired in a procedure call must be released before the procedure returns. The decidability is obtained by a reduction to the reachability problem of Vector Addition Systems with States (VASS).