General decidability theorems for infinite-state systems

Abstract

Over the last few years there has been an increasing research effort directed towards the automatic verification of infinite state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems), which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a well-ordered and well-founded preorder such that the transition relation is "monotonic" (is a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: reachability; eventuality; and simulation. We also describe how these general principles subsume several decidability results from the literature about timed automata, relational automata, Petri nets, and lossy channel systems.