Thomas Brihaye ; Gilles Geeraerts ; Axel Haddad ; Engel Lefaucheux ; Benjamin Monmege - One-Clock Priced Timed Games with Negative Weights

lmcs:6764 - Logical Methods in Computer Science, August 9, 2022, Volume 18, Issue 3 - https://doi.org/10.46298/lmcs-18(3:17)2022
One-Clock Priced Timed Games with Negative Weights

Authors: Thomas Brihaye ; Gilles Geeraerts ; Axel Haddad ; Engel Lefaucheux ; Benjamin Monmege

    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.


    Volume: Volume 18, Issue 3
    Published on: August 9, 2022
    Accepted on: June 18, 2022
    Submitted on: September 8, 2020
    Keywords: Computer Science - Computer Science and Game Theory,Computer Science - Logic in Computer Science

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