Multi-pushdown systems with budgets

We address the verification problem for concurrent programs modeled as multi-pushdown systems (MPDS). In general, MPDS are Turing powerful and hence come along with undecidability of all basic decision problems. Because of this, several subclasses of MPDS have been proposed and studied in the literature [1]-[4]. In this paper, we propose the class of bounded-budget MPDS where we restrict them in the sense that each stack can perform an unbounded number of context switches if its size is below a given bound, and is restricted to a finite number of context switches when its size is above that bound. We show that the reachability problem for this subclass is PSPACE-complete. Furthermore, we propose a code-to-code translation that inputs a concurrent program P and produces a sequential program P' such that running P under the bounded-budget restriction yields the same set of reachable states as running P'. By leveraging standard sequential analysis tools, we have implemented a prototype tool and applied it on a set of benchmarks, showing the feasibility of our translation.