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Infinite-state energy games

Parosh Aziz Abdulla, Mohamed Faouzi Atig, Piotr Hofman, Richard Mayr, K. Narayan Kumar, Patrick Totzke
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata.  ...  Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional.  ...  Using this connection, we show several (un)decidability results for infinite-state energy games.  ... 
doi:10.1145/2603088.2603100 dblp:conf/csl/AbdullaAHMKT14 fatcat:s77fktljqnb5xj7oepjihinzia

Infinite-State Energy Games [article]

Parosh Aziz Abdulla, Mohamed Faouzi Atig, Piotr Hofman, Richard Mayr, K. Narayan Kumar, Patrick Totzke
2014 arXiv   pre-print
We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata.  ...  Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional.  ...  Using this connection, we show several (un)decidability results for infinite-state energy games.  ... 
arXiv:1405.0628v1 fatcat:4txedyql35drbjkxdbbqgduodq

Energy and Mean-Payoff Games with Imperfect Information [chapter]

Aldric Degorre, Laurent Doyen, Raffaella Gentilini, Jean-François Raskin, Szymon Toruńczyk
2010 Lecture Notes in Computer Science  
The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state.  ...  In an energy game, the weights represent resource consumption and the objective of the game is to maintain the sum of weights always nonnegative.  ...  The game H has a finite state space. Proof. By contradiction, assume that Q H is infinite.  ... 
doi:10.1007/978-3-642-15205-4_22 fatcat:shur3s2nw5f25pa7dtzv6hzovq

Energy and Mean-Payoff Parity Markov Decision Processes [chapter]

Krishnendu Chatterjee, Laurent Doyen
2011 Lecture Notes in Computer Science  
While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs.  ...  We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for meanpayoff parity MDPs, the problem is solvable  ...  An MDP can be viewed as the arena of a game played for infinitely many rounds from a state q 0 ∈ Q as follows.  ... 
doi:10.1007/978-3-642-22993-0_21 fatcat:vqqlf5mccndlvn4k2rlkms3ptq

Games and Markov Decision Processes with Mean-Payoff Parity and Energy Parity Objectives [chapter]

Krishnendu Chatterjee, Laurent Doyen
2012 Lecture Notes in Computer Science  
In this paper we survey results of two-player games on graphs and Markov decision processes with parity, mean-payoff and energy objectives, and the combination of mean-payoff and energy objectives with  ...  An MDP can be viewed as the arena of a game played for infinitely many rounds from a state q 0 ∈ Q as follows.  ...  Games with mean-payoff parity and energy parity objectives Mean-payoff parity games were first studied in [9] and it was shown that winning strategies for player 1 require infinite memory in general.  ... 
doi:10.1007/978-3-642-25929-6_3 fatcat:ehqil7hdpvh7rnfwuliovhaul4

Energy Parity Games [article]

Krishnendu Chatterjee, Laurent Doyen
2012 arXiv   pre-print
Energy parity games are infinite two-player turn-based games played on weighted graphs.  ...  infinite memory in mean-payoff parity games.  ...  In each round, the player owning the current state chooses an outgoing edge to a successor state, thus the game results in an infinite play.  ... 
arXiv:1001.5183v4 fatcat:yc5j3y7nozg43kwjpiji63aq4e

Energy Parity Games [chapter]

Krishnendu Chatterjee, Laurent Doyen
2010 Lecture Notes in Computer Science  
Energy parity games are infinite two-player turn-based games played on weighted graphs.  ...  be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games.  ...  In each round, the player owning the current state chooses an outgoing edge to a successor state, thus the game results in an infinite play.  ... 
doi:10.1007/978-3-642-14162-1_50 fatcat:d6sj3bzgqveiteh67hsacgmswm

Energy parity games

Krishnendu Chatterjee, Laurent Doyen
2012 Theoretical Computer Science  
Energy parity games are infinite two-player turn-based games played on weighted graphs.  ...  be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games.  ...  In each round, the player owning the current state chooses an outgoing edge to a successor state, thus the game results in an infinite play.  ... 
doi:10.1016/j.tcs.2012.07.038 pmid:23470985 pmcid:PMC3587466 fatcat:d6rhsehnmjhhhdvdma44f4x6sm

Generalized Mean-payoff and Energy Games

Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, Jean-François Raskin, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative.  ...  We prove the finite-memory determinacy of generalized energy games and show the interreducibility of generalized mean-payoff and energy games for finite-memory strategies.  ...  In both cases, better payoff can be obtained with infinite memory: the example of Figure 2 shows a game where all states belong to Player 1.  ... 
doi:10.4230/lipics.fsttcs.2010.505 dblp:conf/fsttcs/ChatterjeeDHR10 fatcat:oemwt4viorcapkpw6ni77jlcoe

Optimal Power Control in Wireless Powered Sensor Networks: A Dynamic Game-Based Approach

Haitao Xu, Chao Guo, Long Zhang
2017 Sensors  
The energy dynamic of sensors is considered as the state of the system, which is denoted by differential equations.  ...  Through numerical simulations, we demonstrate that our algorithm can obtain optimal power control and reach convergence for an infinite horizon. used for sensors which are located far away from energy  ...  Variation of the optimal uplink power in infinite-horizon. Figure 6 . 6 Dynamic of power level (the optimal state trajectory). Figure 7 . 7 Dynamic of revenue level.  ... 
doi:10.3390/s17030547 pmid:28282945 pmcid:PMC5375833 fatcat:csqz7bjdk5e7bizwdo2sdysz6e

First Cycle Games

Benjamin Aminof, Sasha Rubin
2014 Electronic Proceedings in Theoretical Computer Science  
These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games.  ...  We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions.  ...  condition stating that the energy level is always non-negative starting with initial credit W (|V |−1) is cyc-Energy-greedy on A (where cyc-Energy = the energy level is non-negative).  ... 
doi:10.4204/eptcs.146.11 fatcat:7algkzqnejclzby2ib3v4fsp7q

First-cycle games

Benjamin Aminof, Sasha Rubin
2017 Information and Computation  
These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games.  ...  We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions.  ...  condition stating that the energy level is always non-negative starting with initial credit W (|V |−1) is cyc-Energy-greedy on A (where cyc-Energy = the energy level is non-negative).  ... 
doi:10.1016/j.ic.2016.10.008 fatcat:2xyzztjtujawpcg6nmhyimefqm

The Complexity of Multi-Mean-Payoff and Multi-Energy Games [article]

Yaron Velner, Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, Alexander Rabinovich, Jean-Francois Raskin
2012 arXiv   pre-print
Finally we present the first solution of multi-meanpayoff games with infinite-memory strategies.  ...  We prove the finite-memory determinacy of multi-energy games and show the inter-reducibility of multimean-payoff and multi-energy games for finite-memory strategies.  ...  Multi-Energy Games In this section, we study the determinacy and complexity of multi-energy games.  ... 
arXiv:1209.3234v1 fatcat:srcwatjdufhmxat65sp4enfx6a

Energy and Mean-Payoff Parity Markov Decision Processes [article]

Krishnendu Chatterjee, Laurent Doyen
2011 arXiv   pre-print
While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs.  ...  We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP \cap coNP, while for mean-payoff parity MDPs, the problem is  ...  An MDP can be viewed as the arena of a game played for infinitely many rounds from a state q 0 ∈ Q as follows.  ... 
arXiv:1104.2909v1 fatcat:4jvzspc6wzhjlmydumvvhj4tsa

Electronic Voting: How Logic Can Help

Véronique Cortier
2017 International Conference on Implementation and Application of Automata  
Energy games have recently attracted a lot of attention.  ...  state.  ... 
dblp:conf/wia/Cortier17 fatcat:y6xnhnub75fgxm4wej6v2g7kee
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