On computing reachability sets of process rewrite systems

Abstract

We consider the problem of symbolic reachability analysis of a class of term rewrite systems called Process Rewrite Systems (PRS). A PRS can be seen as the union of two mutually interdependent sets of term rewrite rules: a prefix rewrite system (or, equivalently, a pushdown system), and a multiset rewrite system (or, equivalently, a Petri net). These systems are natural models for multithreaded programs with dynamic creation of concurrent processes and recursive procedure calls. We propose a generic framework based on tree automata allowing to combine (finite-state automata based) procedures for the reachability analysis of pushdown systems with (linear arithmetics/semilinear sets based) procedures for the analysis of Petri nets in order to analyze PRS models. We provide a construction which is parametrized by such procedures and we show that it can be instantiated to (1) derive procedures for constructing the (exact) reachability sets of significant classes of PRS, (2) derive various approximate algorithms, or exact semi-algorithms, for the reachability analysis of PRS obtained by using existing symbolic reachability analysis techniques for Petri nets and counter automata. © Springer-Verlag Berlin Heidelberg 2005.