Model Checking and Modular Veri cation

We describe a framework for compositional veri cation of nite state processes The framework is based on two ideas a subset of the logic CTL for which satisfaction is preserved under composition and a preorder on structures which captures the relation between a component and a system containing the component Satisfaction of a formula in the logic corresponds to being below a particular structure a tableau for the formula in the preorder We show how to do assume guarantee style reasoning within this framework In addition we demonstrate e cient methods for model checking in the logic and for checking the preorder in several special cases We have implemented a system based on these methods and we use it to give a compositional veri cation of a CPU controller