Decidability of approximation for non-negative-weight weighted timed games

Establish the decidability of the Approximation problem for weighted timed games whose transition and location weights are non-negative, thereby extending the decidability result proved for time-bounded weighted timed games to the non-negative-weight setting.

Background

Weighted timed games have an Approximation problem asking whether the game value can be computed to arbitrary precision. General weighted timed games admit undecidability results for both exact value computation and approximation. The paper proves that approximation becomes decidable under a time-boundedness assumption, using convergence of the value iteration algorithm and an explicit convergence-rate bound.

The conclusion identifies decidability for weighted timed games with non-negative weights as the main unresolved problem. The authors note that, in this setting, time spent in positively weighted locations is effectively bounded by any greedy upper bound on the value, suggesting that the techniques developed for time-bounded games may help resolve the question.