Analyzing Asynchronous Programs with Preemption

Abstract

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).