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 the degree of boolean functions as polynomials over mathbb z _m"):
  Abstract: Polynomial representations of Boolean functions over various rings such as $\mathbb{Z}$ and $\mathbb{Z}_m$ have been studied since Minsky and Papert (1969). From then on, they have been employed in a large variety of fields including communication complexity, circuit complexity, learning theory, coding theory and so on. For any integer $m\ge2$, each Boolean function has a unique multilinear polynomial representation over ring $\mathbb Z_m$. The degree of such polynomial is called modulo-$m$ degree, denoted as $\mathrm{deg}_m(\cdot)$. #R##N#In this paper, we discuss the lower bound of modulo-$m$ degree of Boolean functions. When $m=p^k$ ($k\ge 1$) for some prime $p$, we give a tight lower bound that $\mathrm{deg}_m(f)\geq k(p-1)$ for any non-degenerated function $f:\{0,1\}^n\to\{0,1\}$, provided that $n$ is sufficient large. When $m$ contains two different prime factors $p$ and $q$, we give a nearly optimal lower bound for any symmetric function $f:\{0,1\}^n\to\{0,1\}$ that $\mathrm{deg}_m(f) \geq \frac{n}{2+\frac{1}{p-1}+\frac{1}{q-1}}$. #R##N#The idea of the proof is as follows. First we investigate properties of polynomial representation of $\mathsf{MOD}$ function, then use it to span symmetric Boolean functions to prove the lower bound for symmetric functions, when $m$ is a prime power. Afterwards, Ramsey Theory is applied in order to extend the bound from symmetric functions to non-degenerated ones. Finally, by showing that $\mathrm{deg}_p(f)$ and $\mathrm{deg}_q(f)$ cannot be small simultaneously, the lower bound for symmetric functions can be obtained when $m$ is a composite but not prime power.

Includes members:
  Member "a tighter bound on the number of relevant variables in a bounded degree boolean function":
    also connected through other hyperedges:
      (none)
  Member "strong direct product theorems for quantum communication and query complexity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a new minimax theorem for randomized algorithms")
  Member "on the communication complexity of xor functions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "communication lower bounds using dual polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a nearly optimal lower bound on the approximate degree of ac 0")

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)