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 "a duality between depth three formulas and approximation by depth two"):
  Abstract: We establish an explicit link between depth-3 formulas and one-sided approximation by depth-2 formulas, which were previously studied independently. Specifically, we show that the minimum size of depth-3 formulas is (up to a factor of n) equal to the inverse of the maximum, over all depth-2 formulas, of one-sided-error correlation bound divided by the size of the depth-2 formula, on a certain hard distribution. We apply this duality to obtain several consequences: #R##N#1. Any function f can be approximated by a CNF formula of size $O(\epsilon 2^n / n)$ with one-sided error and advantage $\epsilon$ for some $\epsilon$, which is tight up to a constant factor. #R##N#2. There exists a monotone function f such that f can be approximated by some polynomial-size CNF formula, whereas any monotone CNF formula approximating f requires exponential size. #R##N#3. Any depth-3 formula computing the parity function requires $\Omega(2^{2 \sqrt{n}})$ gates, which is tight up to a factor of $\sqrt n$. This establishes a quadratic separation between depth-3 circuit size and depth-3 formula size. #R##N#4. We give a characterization of the depth-3 monotone circuit complexity of the majority function, in terms of a natural extremal problem on hypergraphs. In particular, we show that a known extension of Turan's theorem gives a tight (up to a polynomial factor) circuit size for computing the majority function by a monotone depth-3 circuit with bottom fan-in 2. #R##N#5. AC0[p] has exponentially small one-sided correlation with the parity function for odd prime p.

Includes members:
  Member "addition is exponentially harder than counting for shallow monotone circuits":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "beyond natural proofs hardness magnification and locality")
  Member "the average sensitivity of bounded depth formulas":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "improved pseudorandom generators from pseudorandom multi switching lemmas")
  Member "formulas vs circuits for small distance connectivity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "an improved homomorphism preservation theorem from lower bounds in circuit 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)