Predecessor Sets of Dynamic Pushdown Networks with Tree-Regular Constraints

Dynamic Pushdown Networks (DPNs) are a model for parallel programs with (recursive) procedures and process creation. The goal of this paper is to develop generic techniques for more expressive reachability analysis of DPNs. In the first part of the paper we introduce a new tree-based view on executions. Traditional interleaving semantics model executions by totally ordered sequences. Instead, we model an execution by a partially ordered set of rule applications, that only specifies the per-process ordering and the causality due to process creation, but no ordering between rule applications on processes that run in parallel. Tree-based executions allow us to compute predecessor sets of regular sets of DPN configurations relative to (tree-) regular constraints on executions. The corresponding problem for interleaved executions is not effective. In the second part of the paper, we extend DPNs with (well-nested) locks. We generalize Kahlon and Gupta's technique of acquisition histories to DPNs, and apply the results of the first part of this paper to compute lock-sensitive predecessor sets.