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 "depth 4 lower bounds determinantal complexity a unified approach"):
  Abstract: Tavenas has recently proved that any n^{O(1)}-variate and degree n polynomial in VP can be computed by a depth-4 circuit of size 2^{O(\sqrt{n}\log n)}. So to prove VP not equal to VNP, it is sufficient to show that an explicit polynomial in VNP of degree n requires 2^{\omega(\sqrt{n}\log n)} size depth-4 circuits. Soon after Tavenas's result, for two different explicit polynomials, depth-4 circuit size lower bounds of 2^{\Omega(\sqrt{n}\log n)} have been proved Kayal et al. and Fournier et al. In particular, using combinatorial design Kayal et al.\ construct an explicit polynomial in VNP that requires depth-4 circuits of size 2^{\Omega(\sqrt{n}\log n)} and Fournier et al.\ show that iterated matrix multiplication polynomial (which is in VP) also requires 2^{\Omega(\sqrt{n}\log n)} size depth-4 circuits. #R##N#In this paper, we identify a simple combinatorial property such that any polynomial f that satisfies the property would achieve similar circuit size lower bound for depth-4 circuits. In particular, it does not matter whether f is in VP or in VNP. As a result, we get a very simple unified lower bound analysis for the above mentioned polynomials. #R##N#Another goal of this paper is to compare between our current knowledge of depth-4 circuit size lower bounds and determinantal complexity lower bounds. We prove the that the determinantal complexity of iterated matrix multiplication polynomial is \Omega(dn) where d is the number of matrices and n is the dimension of the matrices. So for d=n, we get that the iterated matrix multiplication polynomial achieves the current best known lower bounds in both fronts: depth-4 circuit size and determinantal complexity. To the best of our knowledge, a \Theta(n) bound for the determinantal complexity for the iterated matrix multiplication polynomial was known only for constant d>1 by Jansen.

Includes members:
  Member "arithmetic circuits with locally low algebraic rank":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "constructing faithful homomorphisms over fields of finite characteristic")
  Member "sums of products of polynomials in few variables lower bounds and polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing")
  Member "the limits of depth reduction for arithmetic formulas it s all about the top fan in":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing")
  Member "improved bounds for reduction to depth 4 and depth 3":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "lower bounds for matrix factorization")
  Member "arithmetic circuits the chasm at depth four gets wider":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "lower bounds for matrix factorization")

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)