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 "polynomial time algorithms for branching markov decision processes and probabilistic min max polynomial bellman equations"):
  Abstract: We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding size of the system of equations and in log(1/epsilon), where epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We establish this result using a generalization of Newton's method which applies to maxPPSs and minPPSs, even though the underlying functions are only piecewise-differentiable. This generalizes our recent work which provided a P-time algorithm for purely probabilistic PPSs. #R##N#These equations form the Bellman optimality equations for several important classes of infinite-state Markov Decision Processes (MDPs). Thus, as a corollary, we obtain the first polynomial time algorithms for computing to within arbitrary desired precision the optimal value vector for several classes of infinite-state MDPs which arise as extensions of classic, and heavily studied, purely stochastic processes. These include both the problem of maximizing and mininizing the termination (extinction) probability of multi-type branching MDPs, stochastic context-free MDPs, and 1-exit Recursive MDPs. #R##N#Furthermore, we also show that we can compute in P-time an epsilon-optimal policy for both maximizing and minimizing branching, context-free, and 1-exit-Recursive MDPs, for any given desired epsilon > 0. This is despite the fact that actually computing optimal strategies is Sqrt-Sum-hard and PosSLP-hard in this setting. #R##N#We also derive, as an easy consequence of these results, an FNP upper bound on the complexity of computing the value (within arbitrary desired precision) of branching simple stochastic games (BSSGs).

Includes members:
  Member "polynomial time algorithms for multi type branching processes and stochastic context free grammars":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "greatest fixed points of probabilistic min max polynomial equations and reachability for branching markov decision processes")
  Member "approximating the termination value of one counter mdps and stochastic games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "deciding fast termination for probabilistic vass with nondeterminism")
  Member "computing the least fixed point of positive polynomial systems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "stochastic context free grammars regular languages and newton s method")
  Member "linear encodings of bounded ltl model checking":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "an abstraction free method for multi robot temporal logic optimal control synthesis")
  Member "model checking probabilistic pushdown automata":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "deciding fast termination for probabilistic vass with nondeterminism")

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.CC(Computational Complexity)