Checking for Fair Simulation in Models with B uchiFairness

Many approaches to overcoming the problem of high space requirements in model checking are based on the simulation preorder. This preorder relates the system model to some reduced model, provided that the reduced model contains all the behaviors of the system model. Reduction techniques often add unrealistic behaviors to the reduced model. Fairness constraints can then be added to exclude these behaviors from consideration during veriication. The simulation preorder, in its original form, does not handle fairness constraints. Fair simulation preorders that extend the simulation preorder by referring only to the fair behaviors of the models are therefore desirable. A deenition of fair simulation was introduced in HKR97]. The deenition is accompanied by an algorithm for checking fair simulation in models with fairness constraints. In this work we suggest an improved algorithm for computing the fair simulation preorder. Our algorithm is signiicantly simpler than the one in HKR97] and therefore easy to implement. It has the same time complexity as the previous algorithm, and a better space complexity. Furthermore, it provides a counterexample in case the reduced model does not contain all the fair behaviors of the system model. Our algorithm is based on a game characterization of the fair simulation preorder. It works in time complexity of O(n 3) and space complexity of O(n), where n is the product of the model sizes.