human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "hyperplane separation technique for multidimensional mean payoff games"):
  Abstract: We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types of strategies are relevant: global strategies, that depend on the entire global history; and modular strategies, that have only local memory and thus do not depend on the context of invocation. We present solutions to several fundamental algorithmic questions and our main contributions are as follows: (1) We show that finite-state multi-dimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of the weight is fixed; whereas if the number of dimensions is arbitrary, then problem is already known to be coNP-complete. (2) We show that pushdown graphs with multi-dimensional mean-payoff objectives can be solved in polynomial time. (3) For pushdown games under global strategies both single and multi-dimensional mean-payoff objectives problems are known to be undecidable, and we show that under modular strategies the multi-dimensional problem is also undecidable (whereas under modular strategies the single dimensional problem is NP-complete). We show that if the number of modules, the number of exits, and the maximal absolute value of the weight is fixed, then pushdown games under modular strategies with single dimensional mean-payoff objectives can be solved in polynomial time, and if either of the number of exits or the number of modules is not bounded, then the problem is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for finite-state multi-dimensional mean-payoff games or pushdown games under modular strategies with single-dimensional mean-payoff objectives would imply the solution of the long-standing open problem of fixed parameter tractability of parity games.

Includes members:
  Member "undecidability of two dimensional robot games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "bounding average energy games")
  Member "fixed dimensional energy games are in pseudo polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "games where you can play optimally with finite memory")
  Member "synthesis from ltl specifications with mean payoff objectives":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "perfect information stochastic games with generalized mean payoff objectives")
  Member "efficient controller synthesis for consumption games with multiple resource types":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "energy mean payoff games")
  Member "the complexity of multi mean payoff and multi energy games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "games where you can play optimally with finite memory")
  Member "mean payoff pushdown games":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "bounding average energy games")
  Member "the complexity of mean payoff automaton expression":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "decidable weighted expressions with presburger combinators")
  Member "qualitative reachability in stochastic bpa games":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "reachability for branching concurrent stochastic games")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.GT(Computer Science and Game Theory)