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## Limit Your Consumption! Finding Bounds in Average-energy Games?

### Citations

292 | Tree automata, mu-calculus and determinacy.
- Emerson, Jutla
- 1991
(Show Context)
Citation Context ..., and only if, there is a there is a cap such that Player 0 wins (A,Recharge(w, cap)). First, assume Player 0 has a winning strategy for the parity game, which we can assume w.l.o.g. to be positional =-=[14,21]-=-. Let W be the largest absolute weight in the image of w and define cap = (|V | − 1) ·W . We claim that 12 σ is a winning strategy for Player 0 in (A,Recharge(w, cap)). Assume it is not: then, there i... |

115 |
Positional strategies for mean payoff games.
- Ehrenfeucht, Mycielski
- 1979
(Show Context)
Citation Context ...t+ 1. 9 5. ρ ∈ AvgRecharge(w, cap, t) if, and only if, ρ′ ∈ MeanPayoff(w′, t). Thus, we have (A,AvgRecharge(w, cap, t)) ≤M (A ×M,MeanPayoff(w′, t)). Hence, positional determinacy of mean-payoff games =-=[12]-=-, Lemma 1, and meanpayoff games being solvable in pseudo-polynomial time [26] yield the exponential time algorithm. uunionsq An application of Lemma 1 additionally yields an upper bound on the necessa... |

78 |
Games with forbidden positions.
- Mostowski
- 1991
(Show Context)
Citation Context ..., and only if, there is a there is a cap such that Player 0 wins (A,Recharge(w, cap)). First, assume Player 0 has a winning strategy for the parity game, which we can assume w.l.o.g. to be positional =-=[14,21]-=-. Let W be the largest absolute weight in the image of w and define cap = (|V | − 1) ·W . We claim that 12 σ is a winning strategy for Player 0 in (A,Recharge(w, cap)). Assume it is not: then, there i... |

60 | Mean-payoff parity games.
- Chatterjee, Henzinger, et al.
- 2005
(Show Context)
Citation Context ...0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games [2,9,22] and objectives such as mean-payoff [7,24,26] and energy =-=[4,10,18]-=- have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether Player 0 wins the game and on memory requirements. In mean-payoff g... |

57 | Better quality in synthesis through quantitative objectives
- Bloem, Chatterjee, et al.
- 2009
(Show Context)
Citation Context ...gy has the desired property when starting at the initial vertex v0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games =-=[2,9,22]-=- and objectives such as mean-payoff [7,24,26] and energy [4,10,18] have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether P... |

22 |
From liveness to promptness
- Kupferman, Piterman, et al.
(Show Context)
Citation Context ...a set of bounds that allow Player 0 to win a quantitative 3 game, e.g., for multi-dimensional energy games with upper bounds [18] and for games with objectives in parameterized generalizations of LTL =-=[1,16,20,25]-=-. 2 Definitions An arena A = (V, V0, V1, E, vI) consists of a finite directed graph (V,E) without terminal vertices, a partition V = V0unionmultiV1 of the vertices, and an initial vertex vI ∈ V . Vert... |

19 | Faster algorithms for mean-payoff games
- Brim, Chaloupka, et al.
(Show Context)
Citation Context ... the initial vertex v0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games [2,9,22] and objectives such as mean-payoff =-=[7,24,26]-=- and energy [4,10,18] have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether Player 0 wins the game and on memory requireme... |

13 | The bad match, a total reward stochastic game, Operations Research Spektrum 9
- Thuijsman, Vrieze
- 1987
(Show Context)
Citation Context ...he maximal energy level allows to improve the average energy level and memory can be traded for smaller upper bounds and vice versa. Related work. The average energy objective was first introduced in =-=[23]-=- under the name total-reward but has until recently not undergone a systematic study. Independently, it was studied (under the name total-payoff) for Markov decision processes and stochastic games [3]... |

9 | The complexity of multi-mean-payoff and multi-energy games
- Velner, Chatterjee, et al.
(Show Context)
Citation Context ... the initial vertex v0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games [2,9,22] and objectives such as mean-payoff =-=[7,24,26]-=- and energy [4,10,18] have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether Player 0 wins the game and on memory requireme... |

8 |
Jǐŕı Srba. Infinite runs in weighted timed automata with energy constraints
- Bouyer, Fahrenberg, et al.
- 2008
(Show Context)
Citation Context ...0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games [2,9,22] and objectives such as mean-payoff [7,24,26] and energy =-=[4,10,18]-=- have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether Player 0 wins the game and on memory requirements. In mean-payoff g... |

8 | Efficient controller synthesis for consumption games with multiple resource types
- Brázdil, Chatterjee, et al.
- 2012
(Show Context)
Citation Context ...recharge the energy to some given capacity. All other edges have non-positive cost, i.e., they only decrease the energy level or leave it unchanged. This is reminiscent of so-called consumption games =-=[6]-=-, where Player 0 picks the new energy level while traversing a recharge edge. There, one is interested in which initial energy levels allow Player 0 to win and to compute upper bounds on the recharge ... |

7 |
Parametric linear dynamic logic
- Faymonville, Zimmermann
- 2014
(Show Context)
Citation Context ...a set of bounds that allow Player 0 to win a quantitative 3 game, e.g., for multi-dimensional energy games with upper bounds [18] and for games with objectives in parameterized generalizations of LTL =-=[1,16,20,25]-=-. 2 Definitions An arena A = (V, V0, V1, E, vI) consists of a finite directed graph (V,E) without terminal vertices, a partition V = V0unionmultiV1 of the vertices, and an initial vertex vI ∈ V . Vert... |

5 |
and Jiŕı Srba. Energy games in multiweighted automata
- Fahrenberg, Juhl, et al.
- 2011
(Show Context)
Citation Context ...e energy, which is the model we consider in this paper. Several other games with combined objectives have been introduced such as mean-payoff parity [11], energy-parity [10], multi-dimensional energy =-=[15]-=- and multi-dimensional mean-payoff [24]. In [6], consumption games are studied where edges only have negative weights, and some distinguished edges recharge the energy to a level determined by Player ... |

5 | Parameterized linear temporal logics meet costs: Still not costlier than LTL. 2015. Accepted for publication at GandALF 2015. Available at arxiv.org/abs/1505.06953
- Zimmermann
(Show Context)
Citation Context ...a set of bounds that allow Player 0 to win a quantitative 3 game, e.g., for multi-dimensional energy games with upper bounds [18] and for games with objectives in parameterized generalizations of LTL =-=[1,16,20,25]-=-. 2 Definitions An arena A = (V, V0, V1, E, vI) consists of a finite directed graph (V,E) without terminal vertices, a partition V = V0unionmultiV1 of the vertices, and an initial vertex vI ∈ V . Vert... |

4 | Markov decision processes and stochastic games with total effective payoff, RUTCOR Research report
- Boros, Elbassioni, et al.
(Show Context)
Citation Context ...23] under the name total-reward but has until recently not undergone a systematic study. Independently, it was studied (under the name total-payoff) for Markov decision processes and stochastic games =-=[3]-=-, and [5] presented a comprehensive investigation into the problem in the deterministic case. The latter also considered the extensions where the average-energy objective is combined with bounds on th... |

4 | Optimal bounds for multiweighted and parametrised energy games
- Juhl, Larsen, et al.
- 2013
(Show Context)
Citation Context ...0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games [2,9,22] and objectives such as mean-payoff [7,24,26] and energy =-=[4,10,18]-=- have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether Player 0 wins the game and on memory requirements. In mean-payoff g... |

3 |
François Laroussinie. Model checking probabilistic timed automata with one or two clocks
- Jurdzinski, Sproston
(Show Context)
Citation Context ...state to continue at. Player 0 wins if the energy level is exactly zero at some point, at which she has to move to the sink state. Otherwise, Player 1 wins. Solving countdown games is ExpTimecomplete =-=[19]-=-. The reduction we present below is a straightforward adaption of the reduction from countdown games to average-energy games [5]. 10 Lemma 4. Solving average-bounded recharge games is ExpTime-hard. Pr... |

2 |
Jean-François Raskin, and PierreAlain Reynier. Automatic synthesis of robust and optimal controllers — an industrial case study
- Cassez, Jessen, et al.
- 2009
(Show Context)
Citation Context ...reas in energy games the goal is to keep the accumulated energy within given bounds. Recently, the average-energy objective was introduced [5] to capture the specification in an industrial case study =-=[8]-=-. In this study, the authors synthesize a controller to operate an oil pump using timed games and Uppaal TiGA. The controller has to keep the amount of oil in an accumulator within given bounds while ... |

2 | 2013): Automated Synthesis of Reliable and Efficient Systems Through Game Theory: A Case Study
- Randour
(Show Context)
Citation Context ...gy has the desired property when starting at the initial vertex v0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games =-=[2,9,22]-=- and objectives such as mean-payoff [7,24,26] and energy [4,10,18] have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether P... |

1 | Infinite runs in recharge automata
- Ejsing-Dunn, Fontani
- 2013
(Show Context)
Citation Context ... energy. 4 Finding Bounds in Average-bounded Recharge Games In this section, we study a variation of energy games called recharge games (the name is inspired by recharge automata, first introduced in =-=[13]-=-). In such games, there are designated recharge edges that recharge the energy to some given capacity. All other edges have non-positive cost, i.e., they only decrease the energy level or leave it unc... |

1 |
The complexity of mean payoff games on graphs. TCS
- Zwick, Paterson
- 1996
(Show Context)
Citation Context ... the initial vertex v0. However, note that the strategy requires memory to implement, as its choices depend on the current energy level. Quantitative games [2,9,22] and objectives such as mean-payoff =-=[7,24,26]-=- and energy [4,10,18] have attracted considerable attention recently. The focus has been on establishing the computational complexity of deciding whether Player 0 wins the game and on memory requireme... |