Simple Priced Timed Games Are Not That Simple

TL;DR

This paper investigates simple priced timed games with one clock and arbitrary weights, demonstrating that optimal values can be computed in exponential time and extending results to more general classes.

Contribution

It introduces an exponential-time algorithm for simple priced timed games with one clock and arbitrary weights, and extends findings to reset-acyclic priced timed games.

Findings

Optimal values for simple priced timed games can be computed in exponential time.

One-clock priced timed games are determined.

Results can be used to solve 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 modeling the costs 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 (positive and negative) weights and show that, for an important subclass of theirs (the so-called simple priced timed games), one can compute, in exponential 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 reset-acyclic priced timed games (with arbitrary weights and one-clock).