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

It is known that pushdown processes have a decidable monadic second-order t heory (Muller and Schupp, Theoret. Comput. Sci. 37 (1985) 51-75) and that t his result covers the model-checking problem for the modal mu-calculus. Unf ortunately, the corresponding decidability procedure is not practical due t o its nonelementary complexity. Recently, however, a very intricate element ary algorithm for model checking the full modal mu-calculus for pushdown pr ocesses 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 de velop here a more structural and transparent elementary algorithm for model -checking infinite sequential processes, including concert-free processes, pushdown processes, and regular graphs, that captures the full modal mu-cal culus as well. Whereas the actual model-checking algorithm simply resorts t o backtracking in order to capture alternation, the corresponding correctne ss proof requires to introduce the stronger framework of dynamic environmen ts which are modelled by finite-state automata. (C) 1999 Elsevier Science B .V. All rights reserved.