Optimal Bounds for Multiweighted and Parametrised Energy Games
Multiweighted energy games are two-player multiweighted games that concern the existence of infinite runs subject to a vector of lower and upper bounds on the accumulated weights along the run. We assume an unknown upper bound and calculate the set of vectors of upper bounds that allow an infinite run to exist. For both a strict and a weak upper bound we show how to construct this set by employing results from previous works, including an algorithm given by Valk and Jantzen for finding the set of minimal elements of an upward closed set. Additionally, we consider energy games where the weight of some transitions is unknown, and show how to find the set of suitable weights using the same algorithm.
KeywordsParametrise Transition Pareto Frontier Winning Strategy Optimal Bound Vacuum Cleaner
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- 1.Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed Automata with Observers under Energy Constraints. In: 13th ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2010), pp. 61–70. ACM (2010)Google Scholar
- 7.Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.F.: Generalized Mean-payoff and Energy Games. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). LIPIcs, vol. 8, pp. 505–516. Schloss Dagstuhl–Leibniz-Zentrum für Informatik (2010)Google Scholar