Symbolic Model Checking

Abstract

In the previous chapter, we equated a CTL formula with the set of states in which the formula is true. We showed how the CTL operators can thus be characterized as fixed points of certain continuous functionals in the lattice of subsets, and how these fixed points can be computed iteratively. This provides us with a model checking algorithm for CTL, but requires us to build a finite Kripke model for our system and hence leads us to the state explosion problem. In this chapter, we will explore a method of model checking that avoids the state explosion problem in some cases by representing the Kripke model implicitly with a Boolean formula. This allows the CTL model checking algorithm to be implemented using well developed automatic techniques for manipulating Boolean formulas. Since the Kripke model is symbolically represented, there is no need to actually construct it as an explicit data structure. Hence, the state explosion problem can be avoided.