Abstract
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. However, the exact complexity in the size of the pushdown system (for a fixed CTL formula) is an open question: it lies somewhere between Pspace and Exptime. To the best of our knowledge, the PMC problem for CTL* has not been investigated so far. In this paper, we show that this problem is 2Expspace-complete. Moreover, 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.
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