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 "tight size degree bounds for sums of squares proofs"):
  Abstract: We exhibit families of $4$-CNF formulas over $n$ variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) $d$ but require SOS proofs of size $n^{\Omega(d)}$ for values of $d = d(n)$ from constant all the way up to $n^{\delta}$ for some universal constant$\delta$. This shows that the $n^{O(d)}$ running time obtained by using the Lasserre semidefinite programming relaxations to find degree-$d$ SOS proofs is optimal up to constant factors in the exponent. We establish this result by combining $\mathsf{NP}$-reductions expressible as low-degree SOS derivations with the idea of relativizing CNF formulas in [Kraj\'i\v{c}ek '04] and [Dantchev and Riis'03], and then applying a restriction argument as in [Atserias, M\"uller, and Oliva '13] and [Atserias, Lauria, and Nordstr\"om '14]. This yields a generic method of amplifying SOS degree lower bounds to size lower bounds, and also generalizes the approach in [ALN14] to obtain size lower bounds for the proof systems resolution, polynomial calculus, and Sherali-Adams from lower bounds on width, degree, and rank, respectively.

Includes members:
  Member "narrow proofs may be maximally long":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "regular resolution for cnf of bounded incidence treewidth with few long clauses")
  Member "sum of squares proofs and the quest toward optimal algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "the complexity of proving that a graph is ramsey":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sherali adams and the binary encoding of combinatorial principles")
  Member "communication lower bounds via critical block sensitivity":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "hypercontractivity sum of squares proofs and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "approximability and proof complexity":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efficiently learning structured distributions from untrusted batches")

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)