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Limit Your Consumption! Finding Bounds in Average-energy Games | | Kim G. Larsen
; Simon Laursen
; Martin Zimmermann
; | | Date: |
20 Oct 2015 | | Abstract: | Energy games are infinite two-player games played in weight-ed arenas with
quantitative objectives that restrict the consumption of a resource modeled by
the weights, e.g., a battery that is charged and drained. Typically, upper
and/or lower bounds on the battery capacity are part of the problem
description. In this work, we consider the problem of determining upper bounds
on the average accumulated energy or on the capacity while satisfying a given
lower bound, i.e., we do not determine whether a given bound is sufficient to
meet the specification, but if there exists a bound that is sufficient to meet
it.
In the classical setting with positive and negative weights, we show that the
problem of determining the existence of a sufficient bound on the long-run
average accumulated energy can be solved in doubly-exponential time. Then, we
consider recharge games: here, all weights are negative, but there are recharge
edges that recharge the energy to some fixed capacity. We show that bounding
the long-run average energy in such games is complete for exponential time.
Then, we consider the existential version of the problem, which turns out to be
solvable in polynomial time: here, we ask whether there is a recharge capacity
that allows the system player to win the game.
We conclude by studying tradeoffs between the memory needed to implement
strategies and the bounds they realize. We give an example showing that memory
can be traded for bounds and vice versa. Also, we show that increasing the
capacity allows to lower the average accumulated energy. | | Source: | arXiv, 1510.5774 | | Services: | Forum | Review | PDF | Favorites | |
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