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 "upper bounds for newton s method on monotone polynomial systems and p time model checking of probabilistic one counter automata"):
  Abstract: A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars, probabilistic pushdown automata and recursive Markov chains) is the computation of {\em termination probabilities}, and computing these probabilities in turn boils down to computing the {\em least fixed point} (LFP) solution of a corresponding {\em monotone polynomial system} (MPS) of equations, denoted x=P(x). #R##N#It was shown by Etessami & Yannakakis that a decomposed variant of Newton's method converges monotonically to the LFP solution for any MPS that has a non-negative solution. Subsequently, Esparza, Kiefer, & Luttenberger obtained upper bounds on the convergence rate of Newton's method for certain classes of MPSs. More recently, better upper bounds have been obtained for special classes of MPSs. However, prior to this paper, for arbitrary (not necessarily strongly-connected) MPSs, no upper bounds at all were known on the convergence rate of Newton's method as a function of the encoding size |P| of the input MPS, x=P(x). #R##N#In this paper we provide worst-case upper bounds, as a function of both the input encoding size |P|, and epsilon > 0, on the number of iterations required for decomposed Newton's method (even with rounding) to converge within additive error epsilon > 0 of q^*, for any MPS with LFP solution q^*. Our upper bounds are essentially optimal in terms of several important parameters. #R##N#Using our upper bounds, and building on prior work, we obtain the first P-time algorithm (in the standard Turing model of computation) for quantitative model checking, to within desired precision, of discrete-time QBDs and (equivalently) probabilistic 1-counter automata, with respect to any (fixed) omega-regular or LTL property.

Includes members:
  Member "exact algorithms for solving stochastic games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "acceptable strategy profiles in stochastic games")
  Member "polynomial time algorithms for multi type branching processes and stochastic context free grammars":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "greatest fixed points of probabilistic min max polynomial equations and reachability for branching markov decision processes")
  Member "efficient analysis of probabilistic programs with an unbounded counter":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "long run average behaviour of probabilistic vector addition systems")
  Member "computing the least fixed point of positive polynomial systems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (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-5 (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-6 (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.LO(Logic in Computer Science)