One-Clock Priced Timed Games with Negative Weights

Priced timed games are two-player zero-sum played on priced automata (whose locations and transitions labeled by weights modelling the cost of spending time in a state executing an action, respectively). The goals players to minimise maximise reach target location, respectively. We consider with one clock arbitrary integer show that, for important subclass them (the so-called simple games), can compute, pseudo-polynomial time, optimal values that achieve, their associated strategies. As side results, we also one-clock determined use our result solve more general class negative-reset-acyclic (with clock). decidability status full still remains open.