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 "on polynomial approximations over mathbb z 2 k mathbb z"):
  Abstract: We study approximation of Boolean functions by low-degree polynomials over the ring $\mathbb{Z}/2^k\mathbb{Z}$. More precisely, given a Boolean function $F:\{0,1\}^n \rightarrow \{0,1\}$, define its $k$-lift to be $F_k:\{0,1\}^n \rightarrow \{0,2^{k-1}\}$ by $F_k(x) = 2^{k-F(x)} \pmod {2^k}$. We consider the fractional agreement (which we refer to as $\gamma_{d,k}(F)$) of $F_k$ with degree $d$ polynomials from $\mathbb{Z}/2^k\mathbb{Z}[x_1,\ldots,x_n]$. Our results are the following: #R##N#- Increasing $k$ can help: We observe that as $k$ increases, $\gamma_{d,k}(F)$ cannot decrease. We give two kinds of examples where $\gamma_{d,k}(F)$ actually increases. The first is an infinite family of functions $F$ such that $\gamma_{2d,2}(F) - \gamma_{3d-1,1}(F) \geq \Omega(1)$. The second is an infinite family of functions $F$ such that $\gamma_{d,1}(F)\leq\frac{1}{2}+o(1)$ -- as small as possible -- but $\gamma_{d,3}(F) \geq \frac{1}{2}+\Omega(1)$. #R##N#- Increasing $k$ doesn't always help: Adapting a proof of Green [Comput. Complexity, 9(1):16-38, 2000], we show that irrespective of the value of $k$, the Majority function $\mathrm{Maj}_n$ satisfies $\gamma_{d,k}(\mathrm{Maj}_n) \leq \frac{1}{2}+\frac{O(d)}{\sqrt{n}}$. In other words, polynomials over $\mathbb{Z}/2^k\mathbb{Z}$ for large $k$ do not approximate the majority function any better than polynomials over $\mathbb{Z}/2\mathbb{Z}$. #R##N#We observe that the model we study subsumes the model of non-classical polynomials in the sense that proving bounds in our model implies bounds on the agreement of non-classical polynomials with Boolean functions. In particular, our results answer questions raised by Bhowmick and Lovett [In Proc. 30th Computational Complexity Conf., pages 72-87, 2015] that ask whether non-classical polynomials approximate Boolean functions better than classical polynomials of the same degree.

Includes members:
  Member "nonclassical polynomials as a barrier to polynomial lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "torus polynomials an algebraic approach to acc lower bounds")
  Member "new algorithms and lower bounds for circuits with linear threshold gates":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lower bounds against sparse symmetric functions of acc circuits expanding the reach of sat algorithms")

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)