Model Checking: A Coalgebraic Approach

State explosion problem is the main obstacle of model checking. In this work, we address this problem from a co algebraic point of view. We establish an effective method to prove uniformly the existence of the smallest Kripke structure with respect to bisimilarity, which describes all behaviors of the Kripke structures with no redundancy. We show this smallest Kripke structure generates a minimal one for each given finite Kripke structure and some kind of infinite ones. This method is based on the existence of the final co algebra of a suitable endofunctor and can be generalized smoothly to other co algebraic structures. A naive implementation of this method is developed in Ocaml.