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 "sum of squares lower bounds for refuting any csp"):
  Abstract: Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen literals. Provided the constraint density satisfies $\Delta \gg 1$, such an instance is unsatisfiable with high probability. The \emph{refutation} problem is to efficiently find a proof of unsatisfiability. #R##N#We show that whenever the predicate $P$ supports a $t$-\emph{wise uniform} probability distribution on its satisfying assignments, the sum of squares (SOS) algorithm of degree $d = \Theta(\frac{n}{\Delta^{2/(t-1)} \log \Delta})$ (which runs in time $n^{O(d)}$) \emph{cannot} refute a random instance of $\mathrm{CSP}(P)$. In particular, the polynomial-time SOS algorithm requires $\widetilde{\Omega}(n^{(t+1)/2})$ constraints to refute random instances of CSP$(P)$ when $P$ supports a $t$-wise uniform distribution on its satisfying assignments. Together with recent work of Lee et al. [LRS15], our result also implies that \emph{any} polynomial-size semidefinite programming relaxation for refutation requires at least $\widetilde{\Omega}(n^{(t+1)/2})$ constraints. #R##N#Our results (which also extend with no change to CSPs over larger alphabets) subsume all previously known lower bounds for semialgebraic refutation of random CSPs. For every constraint predicate~$P$, they give a three-way hardness tradeoff between the density of constraints, the SOS degree (hence running time), and the strength of the refutation. By recent algorithmic results of Allen et al. [AOW15] and Raghavendra et al. [RRS16], this full three-way tradeoff is \emph{tight}, up to lower-order factors.

Includes members:
  Member "lower bounds for csp refutation by sdp hierarchies":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "prediction with a short memory")
  Member "the backtracking survey propagation algorithm for solving random k sat problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the sdp value for random two eigenvalue csps")
  Member "strongly refuting random csps below the spectral threshold":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "how to refute a random csp":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "noisy tensor completion via the sum of squares hierarchy":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "complexity theoretic limitations on learning halfspaces":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "sum of squares lower bounds from pairwise independence":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "breaking symmetries to rescue sum of squares the case of makespan scheduling")
  Member "lower bounds on the size of semidefinite programming relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "lifting with simple gadgets and applications to circuit and proof complexity")

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)