Boundedness vs. Unboundedness of Lock Chains: Characterizing Decidability of CFL-Reachability for Threads Communicating via Locks

The problem of Pairwise CFL-reachability is to decide whether two given program locations in different threads are simultaneously reachable in the presence of recursion in threads and scheduling constraints imposed by synchronization primitives. Pairwise CFL-reachability is the core problem underlying concurrent program analysis especially dataflow analysis. Unfortunately, it is undecidable even for the most commonly used synchronization primitive, i.e., mutex locks. Lock usage in concurrent programs can be characterized in terms of lock chains, where a sequence of mutex locks is said to be chained if the scopes of adjacent (nonnested) mutexes overlap. Although pairwise reachability is known to decidable for threads interacting via nested locks, i.e., chains of length one, these techniques don’t extend to programs with non-nested locks used in crucial applications like databases and device drivers. In this paper, we exploit the fact that lock usage patterns in real life programs do not produce unbounded lock chains. For such programs, we show that pairwise CFL-reachability becomes decidable. Towards that end, we formulate small model properties that bound the lengths of paths that need to be traversed in order to reach a given pair of control states. Our new results narrow the decidability gap for pairwise CFL-reachability by providing a more refined characterization for it in terms of boundedness of lock chains rather than the current stateof-the-art, i.e., nestedness of locks (chains of length one).