Model checking the full modal mu-calculus for infinite sequential processes

AbstractIt is known that pushdown processes have a decidable monadic second-order theory (Muller and Schupp, Theoret. Comput. Sci. 37 (1985) 51–;75) and that this result covers the model-checking problem for the modal mu-calculus. Unfortunately, the corresponding decidability procedure is not practical due to its nonelementary complexity. Recently, however, a very intricate elementary algorithm for model checking the full modal mu-calculus for pushdown processes based on games was presented by Walukiewicz (CAV'96, Lecture Notes in Computer Science, vol. 1102, Springer, Berlin, 1996, pp. 62–;74). Lifting the classical finite-state model checking technique to second-order, we develop here a more structural and transparent elementary algorithm for model-checking infinite sequential processes, including context-free processes, pushdown processes, and regular graphs, that captures the full modal mu-calculus as well. Whereas the actual model-checking algorithm simply resorts to backtracking in order to capture alternation, the corresponding correctness proof requires to introduce the stronger framework of dynamic environments which are modelled by finite-state automata