Contextual locking for dynamic pushdown networks

Contextual locking is a scheme for synchronizing between possibly recursive processes that has been proposed by Chadha et al. recently. Contextual locking allows for arbitrary usage of locks within the same procedure call and Chadha et al. show that control-point reachability for two processes adhering to contextual locking is decidable in polynomial time. Here, we complement these results. We show that in presence of contextual locking, control-point reachability becomes PSPACE-hard, already if the number of processes is increased to three. On the other hand, we show that PSPACE is both necessary and sufficient for deciding control-point reachability of k processes for k > 2, and that this upper bound remains valid even if dynamic spawning of new processes is allowed. Furthermore, we consider the problem of regular reachability, i.e., whether a configuration within a given regular set can be reached. Here, we show that this problem is decidable for recursive processes with dynamic thread creation and contextual locking. Finally, we generalize this result to processes that additionally use a form of join operations.