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Communication Dans Un Congrès Année : 2014

Adding Negative Prices to Priced Timed Games

Résumé

Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et al. and Alur, Bernadsky, and Mad-husudan independently proposed algorithms to solve PTGs with non-negative prices under certain divergence restriction over prices. Brihaye, Bruy ere, and Raskin later provided a justification for such a restriction by showing the undecidability of the optimal strategy synthesis problem in the absence of this divergence restriction. This problem for PTGs with one clock has long been conjectured to be in polynomial time, however the current best known algorithm, by Hansen, Ibsen-Jensen, and Mil-tersen, is exponential. We extend this picture by studying PTGs with both negative and positive prices. We refine the undecidability results for optimal strategy synthesis problem, and show undecidability for several variants of optimal reachability cost objectives including reachability cost, time-bounded reachability cost, and repeated reachability cost objectives. We also identify a subclass with bi-valued price-rates and give a pseudo-polynomial (polynomial when prices are nonnegative) algorithm to partially answer the conjecture on the complexity of one-clock PTGs.
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hal-01273480 , version 1 (12-02-2016)

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Thomas Brihaye, Gilles Geeraerts, Shankara Narayanan Krishna, Lakshmi Manasa, Benjamin Monmege, et al.. Adding Negative Prices to Priced Timed Games. 25th International Conference on Concurrency Theory (CONCUR'14), Sep 2014, Rome, Italy. pp.560-575, ⟨10.1007/978-3-662-44584-6_38⟩. ⟨hal-01273480⟩
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