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 "alternation sparsity and sensitivity bounds and exponential gaps"):
  Abstract: $\newcommand{\sp}{\mathsf{sparsity}}\newcommand{\s}{\mathsf{s}}\newcommand{\al}{\mathsf{alt}}$ The well-known Sensitivity Conjecture states that for any Boolean function $f$, block sensitivity of $f$ is at most polynomial in sensitivity of $f$ (denoted by $\s(f)$). The XOR Log-Rank Conjecture states that for any $n$ bit Boolean function, $f$ the communication complexity of a related function $f^{\oplus}$ on $2n$ bits, (defined as $f^{\oplus}(x,y)=f(x\oplus y)$) is at most polynomial in logarithm of the sparsity of $f$ (denoted by $\sp(f)$). A recent result of Lin and Zhang (2017) implies that to confirm the above conjectures it suffices to upper bound alternation of $f$ (denoted $\al(f)$) for all Boolean functions $f$ by polynomial in $\s(f)$ and logarithm of $\sp(f)$, respectively. In this context, we show the following : #R##N#* There exists a family of Boolean functions for which $\al(f)$ is at least exponential in $\s(f)$ and $\al(f)$ is at least exponential in $\log \sp(f)$. En route to the proof, we also show an exponential gap between $\al(f)$ and the decision tree complexity of $f$, which might be of independent interest. #R##N#* As our main result, we show that, despite the above gap between $\al(f)$ and $\log \sp(f)$, the XOR Log-Rank Conjecture is true for functions with the alternation upper bounded by $poly(\log n)$. It is easy to observe that the Sensitivity Conjecture is also true for this class of functions. #R##N#* The starting point for the above result is the observation (derived from Lin and Zhang (2017)) that for any Boolean function $f$ and $m \ge 2$, $deg(f)\le \al(f)deg_2(f)deg_m(f)$ where $deg(f)$, $deg_2(f)$ and $deg_m(f)$ are the degrees of $f$ over $\mathbb{R}$, $\mathbb{F}_2$ and $\mathbb{Z}_m$ respectively. We also show three further applications of this observation.

Includes members:
  Member "on the sensitivity conjecture for disjunctive normal forms":
    also connected through other hyperedges:
      (none)
  Member "sensitivity conjecture and log rank conjecture for functions with small alternating numbers":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sensitivity affine transforms and quantum communication complexity")
  Member "degree and sensitivity tails of two distributions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "improved bounds on fourier entropy and min entropy")
  Member "sensitivity versus certificate complexity of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sensitivity conjecture and log rank conjecture for functions with small alternating numbers")
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "learning circuits with few negations":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "top down induction of decision trees rigorous guarantees and inherent limitations")
  Member "communication is bounded by root of rank":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "theory and practice of data citation")
  Member "fourier sparsity spectral norm and the log rank conjecture":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")

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)