Complexity results on branching-time pushdown model checking

The model checking problem of pushdown systems (PMC problem, for short) against standard branching temporal logics has been intensively studied in the literature. In particular, for the modal μ-calculus, the most powerful branching temporal logic used for verification, the problem is known to be Exptime-complete (even for a fixed formula). The problem remains Exptime-complete also for the logic CTL, which corresponds to a fragment of the alternation-free modal μ-calculus. For the logic , the problem is known to be in 2Exptime. In this paper, we show that the complexity of the PMC problem for  is in fact 2Exptime-complete. Moreover, we give a new optimal algorithm to solve this problem based on automata theoretic techniques. Finally, we prove that the program complexity of the PMC problem against CTL (i.e., the complexity of the problem in terms of the size of the system) is Exptime-complete.