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ONE-CLOCK PRICED TIMED GAMES WITH NEGATIVE WEIGHTS

par Brihaye, Thomas;Geeraerts, Gilles ;Haddad, Axel;Lefaucheux, Engel;Monmege, Benjamin
Référence Logical methods in computer science, 18, 3, page (17:1-17:51)
Publication Publié, 2022

Article révisé par les pairs

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Résumé :

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.