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 "separation of ac 0 oplus formulas and circuits"):
  Abstract: This paper gives the first separation between the power of {\em formulas} and {\em circuits} of equal depth in the $\mathrm{AC}^0[\oplus]$ basis (unbounded fan-in AND, OR, NOT and MOD$_2$ gates). We show, for all $d(n) \le O(\frac{\log n}{\log\log n})$, that there exist {\em polynomial-size depth-$d$ circuits} that are not equivalent to {\em depth-$d$ formulas of size $n^{o(d)}$} (moreover, this is optimal in that $n^{o(d)}$ cannot be improved to $n^{O(d)}$). This result is obtained by a combination of new lower and upper bounds for {\em Approximate Majorities}, the class of Boolean functions $\{0,1\}^n \to \{0,1\}$ that agree with the Majority function on $3/4$ fraction of inputs. #R##N#$\mathrm{AC}^0[\oplus]$ formula lower bound: We show that every depth-$d$ $\mathrm{AC}^0[\oplus]$ formula of size $s$ has a {\em $1/8$-error polynomial approximation} over $\mathbb{F}_2$ of degree $O(\frac{1}{d}\log s)^{d-1}$. This strengthens a classic $O(\log s)^{d-1}$ degree approximation for \underline{circuits} due to Razborov. Since the Majority function has approximate degree $\Theta(\sqrt n)$, this result implies an $\exp(\Omega(dn^{1/2(d-1)}))$ lower bound on the depth-$d$ $\mathrm{AC}^0[\oplus]$ formula size of all Approximate Majority functions for all $d(n) \le O(\log n)$. #R##N#Monotone $\mathrm{AC}^0$ circuit upper bound: For all $d(n) \le O(\frac{\log n}{\log\log n})$, we give a randomized construction of depth-$d$ monotone $\mathrm{AC}^0$ circuits (without NOT or MOD$_2$ gates) of size $\exp(O(n^{1/2(d-1)}))$ that compute an Approximate Majority function. This strengthens a construction of \underline{formulas} of size $\exp(O(dn^{1/2(d-1)}))$ due to Amano.

Includes members:
  Member "the average sensitivity of bounded depth formulas":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "improved pseudorandom generators from pseudorandom multi switching lemmas")
  Member "bounds on the size of small depth circuits for approximating majority":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fourier bounds and pseudorandom generators for product tests")

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)