Approximating the Value of Time-Bounded Weighted Timed Games

The Value Problem for weighted timed games, an extension of timed automata with weights and adversity, consists in determining, given a weighted timed game with a reachability objective and a rational threshold, whether or not the value of the game exceeds the threshold. This problem is known to be undecidable for weighted timed games, i.e., there is no algorithm that can compute the value exactly. A natural alternative is to approximate the value; however, the Approximation problem is also undecidable in general. In this paper, we prove that the Approximation problem is decidable in 4-ExpTime for weighted timed games whose executions are time-bounded.