In this work, we consider Discrete-Time Continuous-Space Dynamic Systems for which we study the computability of the standard semantics of CTL* (CTL, LTL) and provide a variant thereof computable in the sense of Type-2 Theory of Effectivity. In particular, we show how the computable model checking of existentially and universally quantified path formulae of LTL can be reduced to solving, respectively, repeated reachability and persistence problems on a model obtained as a parallel composition of the original one and a non-deterministic B??chi automaton corresponding to the verified LTL formula.
Collins, P., & Zapreev, I. S. (2011). Computable semantics for CTL* on discrete time and continuous space dynamic systems. Int. J. Found. Comput. Sci., 22(4), 801-821. https://doi.org/10.1142/S012905411100843X