Optimal Paths in Weighted Timed Automata

We consider an optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortest-path problem for a finite directed graph. The directed graph we construct is a refinement of the region automaton due to Alur and Dill. We present an exponential time algorithm to solve the shortest-path problem for weighted timed automata starting from a single state, and a doubly-exponential time algorithm to solve this problem starting from a zone of the state space.