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 "the intersection of two halfspaces has high threshold degree"):
  Abstract: The threshold degree of a Boolean function f:{0,1}^n->{-1,+1} is the least degree of a real polynomial p such that f(x)=sgn p(x). We construct two halfspaces on {0,1}^n whose intersection has threshold degree Theta(sqrt n), an exponential improvement on previous lower bounds. This solves an open problem due to Klivans (2002) and rules out the use of perceptron-based techniques for PAC learning the intersection of two halfspaces, a central unresolved challenge in computational learning. We also prove that the intersection of two majority functions has threshold degree Omega(log n), which is tight and settles a conjecture of O'Donnell and Servedio (2003). #R##N#Our proof consists of two parts. First, we show that for any nonconstant Boolean functions f and g, the intersection f(x)^g(y) has threshold degree O(d) if and only if ||f-F||_infty + ||g-G||_infty < 1 for some rational functions F, G of degree O(d). Second, we settle the least degree required for approximating a halfspace and a majority function to any given accuracy by rational functions. #R##N#Our technique further allows us to make progress on Aaronson's challenge (2008) and contribute strong direct product theorems for polynomial representations of composed Boolean functions of the form F(f_1,...,f_n). In particular, we give an improved lower bound on the approximate degree of the AND-OR tree.

Includes members:
  Member "a note on the sign degree of formulas":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "optimal bounds for sign representing the intersection of two halfspaces by polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "communication lower bounds using dual polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the degree of boolean functions as polynomials over mathbb z _m")

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)