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 nearly optimal lower bound on the approximate degree of ac 0"):
  Abstract: The approximate degree of a Boolean function $f \colon \{-1, 1\}^n \rightarrow \{-1, 1\}$ is the least degree of a real polynomial that approximates $f$ pointwise to error at most $1/3$. We introduce a generic method for increasing the approximate degree of a given function, while preserving its computability by constant-depth circuits. #R##N#Specifically, we show how to transform any Boolean function $f$ with approximate degree $d$ into a function $F$ on $O(n \cdot \operatorname{polylog}(n))$ variables with approximate degree at least $D = \Omega(n^{1/3} \cdot d^{2/3})$. In particular, if $d= n^{1-\Omega(1)}$, then $D$ is polynomially larger than $d$. Moreover, if $f$ is computed by a polynomial-size Boolean circuit of constant depth, then so is $F$. #R##N#By recursively applying our transformation, for any constant $\delta > 0$ we exhibit an AC$^0$ function of approximate degree $\Omega(n^{1-\delta})$. This improves over the best previous lower bound of $\Omega(n^{2/3})$ due to Aaronson and Shi (J. ACM 2004), and nearly matches the trivial upper bound of $n$ that holds for any function. Our lower bounds also apply to (quasipolynomial-size) DNFs of polylogarithmic width. #R##N#We describe several applications of these results. We give: #R##N#* For any constant $\delta > 0$, an $\Omega(n^{1-\delta})$ lower bound on the quantum communication complexity of a function in AC$^0$. #R##N#* A Boolean function $f$ with approximate degree at least $C(f)^{2-o(1)}$, where $C(f)$ is the certificate complexity of $f$. This separation is optimal up to the $o(1)$ term in the exponent. #R##N#* Improved secret sharing schemes with reconstruction procedures in AC$^0$.

Includes members:
  Member "on szk and pp":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the power of statistical zero knowledge")
  Member "separations in query complexity based on pointer functions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a tight composition theorem for the randomized query complexity of partial functions")
  Member "dual polynomials for collision and element distinctness":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the power of statistical zero knowledge")
  Member "distribution independent reliable learning":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the extended littlestone s dimension for learning with mistakes and abstentions")
  Member "dual lower bounds for approximate degree and markov bernstein inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "faster private release of marginals on small databases":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the power of factorization mechanisms in local and central differential privacy")
  Member "hardness amplification and the approximate degree of constant depth circuits":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "faster algorithms for privately releasing marginals":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "data dependent differentially private parameter learning for directed graphical models")

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)