Analyzing Asynchronous Programs with Preemption

Multiset pushdown systems have been introduced by Sen and Viswanathan as an adequate model for asynchronous programs where some procedure calls can be stored as tasks to be processed later. The model is a pushdown system supplied with a multiset of pending tasks. Tasks may be added to the multiset at each transition, whereas a task is taken from the multiset only when the stack is empty. In this paper, we consider an extension of these models where tasks may be of different priority level, and can be preempted at any point of their execution by tasks of higher priority. We investigate the control point reachability problem for these models. Our main result is that this problem is decidable by reduction to the reachability problem for a decidable class of Petri nets with inhibitor arcs. We also identify two subclasses of these models for which the control point reachability problem is reducible respectively to the reachability problem and to the coverability problem for Petri nets (without inhibitor arcs).