Branching-Time Temporal Logic and Tree Automata

JJ89] C. Jard and T. Jeron. On-line model-checking for nite linear temporal logic speciications. 6 Conclusions In this paper we showed that tree automata, which have been considered unsuitable for branching-time model checking, provide a neat and optimal framework for branching-time temporal logics and can handle, eeciently, model checking. The crucial point in our method is that when branching-time temporal logics are considered, a wise presentation of the model can save the exponential blow up which is involved in conventional translations of formulas to automata. Moreover, when model checking is considered, and the model is part of the problem input, a wise presentation involves no complexity penalty and suits properly the automata-theoretic framework. In conclusion, introducing an eecient automata-theoretic framework for branching time model checking, the paper both closes the theoretical long-standing gap between linear-time and branching-time temporal logics, and opens the way to practical automata-based model-checking algorithms that have already proved themselves in the context of linear time. Acknowledgment We thank Moshe Vardi for many helpful suggestions and discussions.