All from one, one for all: On model checking using representatives

Abstract

Checking that a given finite state program satisfies a linear temporal logic property is suffering in many cases from a severe space and time explosion. One way to cope with this is to reduce the state graph used for model checking. We define an equivalence relation between infinite sequences, based on infinite traces such that for each equivalence class, either all or none of the sequences satisfy the checked formula. We present an algorithm for constructing a state graph that contains at least one representative sequence for each equivalence class. This allows applying existing model checking algorithms to the reduced state graph rather than on the larger full state graph of the program. It also allows model checking under fairness assumptions, and exploits these assumptions to obtain smaller state graphs. A formula rewriting technique is presented to allow coarser equivalence relation among sequences, such that less representatives are needed.