Dynamic Pushdown Networks

We present a formalization of Dynamic Pushdown Networks (DPNs) and the automata based algorithm for computing backward reachability sets using Isabelle/HOL. Dynamic pushdown networks are an abstract model for multithreaded, interprocedural programs with dynamic thread creation that was presented by Bouajjani, Müller-Olm and Touili in 2005. We formalize the notion of a DPN in Isabelle and describe the algorithm for computing the $pre^*$-set from a regular set of configurations, and prove its correctness. We first give a nondeterministic description of the algorithm, from that we then infer a deterministic one, from which we can generate executable code using Isabelle's code-generation tool.