We describe a framework for compositional verification of finite 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 efficient 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 verification of a CPU controller. 1 Introduction Temporal logic model checking procedures are useful tools for the verification of finite state systems [3, 12, 20]. However, these procedures have traditionally suffered from the state explosion proble...