A Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems 1 Stefan G¨ oller, University of Bremen Anthony Widjaja Lin, Singapore University of Technology and Design 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, Petri nets and PA-processes. A seperate development in the term rewriting community introduced the notion of Ground Tree Rewrite Systems (GTRS), which is a model that strictly extends pushdown systems 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 paper 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, e.g., simpler proofs of known decidability results of verifications problems on PAD. Categories and Subject Descriptors: F.1.1 [Models of Computation]: Automata, Relations between models; F.4.1 [Math- ematical Logic]: Temporal Logic; F.4.2 [Grammars and Other Rewriting Systems]: Parallel rewriting systems; F.4.3 [Formal Languages]: Classes defined by grammars or automata General Terms: Sequentiality, Parallelism, Concurrency, Rewrite Systems, Expressive Power Additional Key Words and Phrases: Rewrite Systems, ground terms, trees, hierarchy ACM Reference Format: G¨ oller, S., Lin, A.W. 2011. Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems. ACM Trans. Comput. Logic V, N, Article A (January YYYY), 27 pages. DOI = 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000 1. INTRODUCTION The study of infinite-state verification has revealed that unbounded recursions and unbounded paral- lelism are two of the most important sources of infinity in computer programs. Infinite-state models with unbounded recursions such as Basic Process Algebra (BPA), and Pushdown Systems (PDS) have been studied for a long time (e.g. [Baeten et al. 1987; Muller and Schupp 1985]). The same can be said about infinite-state models with unbounded parallelism, which include Basic Parallel Pro- cesses (BPP) and Petri nets (PN), e.g. [Christensen 1993; Hack 1976; Esparza and Nielsen 1994]. While these aforementioned models are either purely sequential or purely parallel, there are also models that simultaneously inherit both of these features. A well-known example are PA-processes [Bergstra and Klop 1985], which are a common generalization of BPA and BPP. It is known that all of these models are not Turing-powerful in the sense that decision problems such as reachability are still decidable (e.g. see [Burkart et al. 2001]), which makes them suitable for verification. In his seminal paper [Mayr 2000], Mayr introduced the Process Rewrite Systems (PRS) hierarchy (see leftmost diagram in Figure 1) containing several models of infinite-state systems that generalize 1 An extended abstract of this paper has appeared in the proceedings of CONCUR 2011 [G¨ oller and Lin 2011a]. Anthony W. Lin thanks EPSRC (EP/H026878/1) for their generous support. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. c  YYYY ACM 1529-3785/YYYY/01-ARTA $10.00 DOI 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000 ACM Transactions on Computational Logic, Vol. V, No. N, Article A, Publication date: January YYYY.