Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems

Abstract

In his seminal paper, Mayr introduced the well-known process rewrite systems (PRS) hierarchy, which contains many well-studied classes of infinite-state systems including pushdown systems (PDS), Petri nets, and PA-processes. A separate development in the term rewriting community introduced the notion of ground tree rewrite systems (GTRS), which is a model that strictly extends PDS while still enjoying desirable decidable properties. There have been striking similarities between the verification problems that have been shown decidable (and undecidable) over GTRS and over models in the PRS hierarchy such as PA and PAD processes. It is open to what extent PRS and GTRS are connected in terms of their expressive power. In this article, we pinpoint the exact connection between GTRS and models in the PRS hierarchy in terms of their expressive power with respect to strong, weak, and branching bisimulation. Among others, this connection allows us to give new insights into the decidability results for subclasses of PRS, such as simpler proofs of known decidability results of verifications problems on PAD.