Analysing Infinite-State Systems by Combining Equivalence Reduction and the Sweep-Line Method

Abstract

The sweep-line method is a state space exploration method for on-the-fly verification aimed at systems exhibiting progress. Presence of progress in the system makes it possible to delete certain states during state space generation, which reduces the memory used for storing the states. Unfortunately, the same progress that is used to improve memory performance in state space exploration often leads to an infinite state space: The progress in the system is carried over to the states resulting in infinitely many states only distinguished through the progress. A finite state space can be obtained using equivalence reduction, abstracting away the progress, but in its simplest form this removes the progress property required by the sweep-line method. In this paper we examine a new method for using equivalence relations to obtain a finite set of classes, without compromising the progress property essential for the sweep-line method. We evaluate the new method on two case studies, showing significant improvements in performance, and we briefly discuss the new method in the context of Timed Coloured Petri Nets, where the “increasing global time” semantics can be exploited for more efficient analysis than what is achieved using a “delay” semantics.