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 "how to refute a random csp"):
  Abstract: Let $P$ be a $k$-ary predicate over a finite alphabet. Consider a random CSP$(P)$ instance $I$ over $n$ variables with $m$ constraints. When $m \gg n$ the instance $I$ will be unsatisfiable with high probability, and we want to find a refutation - i.e., a certificate of unsatisfiability. When $P$ is the $3$-ary OR predicate, this is the well studied problem of refuting random $3$-SAT formulas, and an efficient algorithm is known only when $m \gg n^{3/2}$. Understanding the density required for refutation of other predicates is important in cryptography, proof complexity, and learning theory. Previously, it was known that for a $k$-ary predicate, having $m \gg n^{\lceil k/2 \rceil}$ constraints suffices for refutation. We give a criterion for predicates that often yields efficient refutation algorithms at much lower densities. Specifically, if $P$ fails to support a $t$-wise uniform distribution, then there is an efficient algorithm that refutes random CSP$(P)$ instances $I$ whp when $m \gg n^{t/2}$. Indeed, our algorithm will "somewhat strongly" refute $I$, certifying $\mathrm{Opt}(I) \leq 1-\Omega_k(1)$, if $t = k$ then we get the strongest possible refutation, certifying $\mathrm{Opt}(I) \leq \mathrm{E}[P] + o(1)$. This last result is new even in the context of random $k$-SAT. Regarding the optimality of our $m \gg n^{t/2}$ requirement, prior work on SDP hierarchies has given some evidence that efficient refutation of random CSP$(P)$ may be impossible when $m \ll n^{t/2}$. Thus there is an indication our algorithm's dependence on $m$ is optimal for every $P$, at least in the context of SDP hierarchies. Along these lines, we show that our refutation algorithm can be carried out by the $O(1)$-round SOS SDP hierarchy. Finally, as an application of our result, we falsify assumptions used to show hardness-of-learning results in recent work of Daniely, Linial, and Shalev-Shwartz.

Includes members:
  Member "complexity theoretic limitations on learning halfspaces":
    also connected through other hyperedges:
      - Hyperedge HE-1 (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-2 (induced by source paper "breaking symmetries to rescue sum of squares the case of makespan scheduling")
  Member "tensor prediction rademacher complexity and random 3 xor":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "extended formulation lower bounds for refuting random csps")
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "subsampled power iteration a unified algorithm for block models and planted csp s":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "spectral detection on sparse hypergraphs")
  Member "sum of squares proofs and the quest toward optimal algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "from average case complexity to improper learning complexity":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "more data speeds up training time in learning halfspaces over sparse vectors":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")

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)