Applicability of Fair Simulation

In this paper we compare four notions of fair simulation direct delay game and exists Our comparison refers to three main aspects The time complexity of constructing the fair simulation the ability to use it for minimization and the relationship between the fair simulations and universal branching time logics We developed two practical applications that are based on this com parison The rst is an e cient approximated minimization algorithm for the delay game exists simulations The second is a new implemen tation for the assume guarantee modular framework presented in The new implementation signi cantly improves the complexity of the framework