One-Clock Priced Timed Games with Negative Weights

TL;DR

This paper studies one-clock priced timed games with negative weights, showing how to compute optimal strategies for a key subclass in pseudo-polynomial time and establishing determinacy for these games.

Contribution

It introduces a method to compute optimal strategies in simple priced timed games with negative weights and extends results to negative-reset-acyclic games, advancing understanding of one-clock priced timed games.

Findings

Optimal strategies can be computed in pseudo-polynomial time for simple priced timed games.

One-clock priced timed games are determined.

Results apply to negative-reset-acyclic priced timed games.

Abstract

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