Parameter Synthesis for Probabilistic Timed Automata Using Stochastic Game Abstractions

Abstract

We propose a method to synthesise optimal values of timing parameters for probabilistic timed automata, in the sense that the prob- ability of reaching some set of states is either maximised or minimised. Our rst algorithm, based on forward exploration of the symbolic states, can only guarantee parameter values that correspond to upper (resp. lower) bounds on maximum (resp. minimum) reachability probability. To ensure precise reachability probabilities, we adapt the game-based abstraction re nement method. In the parametric setting, our method is able to determine all the possible maximum (or minimum) reachabil- ity probabilities that arise for di erent values of timing parameters, and yields optimal valuations represented as a set of symbolic constraints between parameters.