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 "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"):
  Abstract: We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to syntactically computing $P$, when $C \equiv P$ as formal polynomials. In this paper, we study the question of proving lower bounds for homogeneous depth-$3$ and depth-$4$ arithmetic circuits for functional computation. We prove the following results : #R##N#1. Exponential lower bounds homogeneous depth-$3$ arithmetic circuits for a polynomial in $VNP$. #R##N#2. Exponential lower bounds for homogeneous depth-$4$ arithmetic circuits with bounded individual degree for a polynomial in $VNP$. #R##N#Our main motivation for this line of research comes from our observation that strong enough functional lower bounds for even very special depth-$4$ arithmetic circuits for the Permanent imply a separation between ${\#}P$ and $ACC$. Thus, improving the second result to get rid of the bounded individual degree condition could lead to substantial progress in boolean circuit complexity. Besides, it is known from a recent result of Kumar and Saptharishi [KS15] that over constant sized finite fields, strong enough average case functional lower bounds for homogeneous depth-$4$ circuits imply superpolynomial lower bounds for homogeneous depth-$5$ circuits. #R##N#Our proofs are based on a family of new complexity measures called shifted evaluation dimension, and might be of independent interest.

Includes members:
  Member "proof complexity lower bounds from algebraic circuit complexity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "semi algebraic proofs ips lower bounds and the tau conjecture can a natural number be negative")
  Member "an exponential lower bound for homogeneous depth 5 circuits over finite fields":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing")
  Member "circuit complexity proof complexity and polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "search problems in algebraic complexity gct and hardness of generator for invariant rings")
  Member "on the power of homogeneous depth 4 arithmetic circuits":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new exponential size lower bounds against depth four circuits of bounded individual degree")

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)