human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "addition is exponentially harder than counting for shallow monotone circuits"
  Abstract: Let $U_{k,N}$ denote the Boolean function which takes as input $k$ strings of $N$ bits each, representing $k$ numbers $a^{(1)},\dots,a^{(k)}$ in $\{0,1,\dots,2^{N}-1\}$, and outputs 1 if and only if $a^{(1)} + \cdots + a^{(k)} \geq 2^N.$ Let THR$_{t,n}$ denote a monotone unweighted threshold gate, i.e., the Boolean function which takes as input a single string $x \in \{0,1\}^n$ and outputs $1$ if and only if $x_1 + \cdots + x_n \geq t$. We refer to circuits that are composed of THR gates as monotone majority circuits. #R##N#The main result of this paper is an exponential lower bound on the size of bounded-depth monotone majority circuits that compute $U_{k,N}$. More precisely, we show that for any constant $d \geq 2$, any depth-$d$ monotone majority circuit computing $U_{d,N}$ must have size $\smash{2^{\Omega(N^{1/d})}}$. Since $U_{k,N}$ can be computed by a single monotone weighted threshold gate (that uses exponentially large weights), our lower bound implies that constant-depth monotone majority circuits require exponential size to simulate monotone weighted threshold gates. This answers a question posed by Goldmann and Karpinski (STOC'93) and recently restated by Hastad (2010, 2014). We also show that our lower bound is essentially best possible, by constructing a depth-$d$, size-$2^{O(N^{1/d})}$ monotone majority circuit for $U_{d,N}$. #R##N#As a corollary of our lower bound, we significantly strengthen a classical theorem in circuit complexity due to Ajtai and Gurevich (JACM'87). They exhibited a monotone function that is in AC$^0$ but requires super-polynomial size for any constant-depth monotone circuit composed of unbounded fan-in AND and OR gates. We describe a monotone function that is in depth-$3$ AC$^0$ but requires exponential size monotone circuits of any constant depth, even if the circuits are composed of THR gates.

Connected through hyperedge HE-1 (induced by source paper "beyond natural proofs hardness magnification and locality"):
  with members:
    - "conspiracies between learning algorithms circuit lower bounds and pseudorandomness"

Connected through hyperedge HE-2 (induced by source paper "a duality between depth three formulas and approximation by depth two"):
  with members:
    - "the average sensitivity of bounded depth formulas"
    - "formulas vs circuits for small distance connectivity"

Connected through hyperedge HE-3 (induced by source paper "small extended formulation for knapsack cover inequalities from monotone circuits"):
  with members:
    - "extension complexity of independent set polytopes"
    - "a primal dual approximation algorithm for min sum single machine scheduling problems"
    - "a 4 approximation for scheduling on a single machine with general cost function"
    - "lower bounds on the size of semidefinite programming relaxations"
    - "approximate constraint satisfaction requires large lp relaxations"
    - "the matching polytope has exponential extension complexity"
    - "approximation limits of linear programs beyond hierarchies"
    - "the geometry of scheduling"

Connected through hyperedge HE-4 (induced by source paper "computing majority by constant depth majority circuits with low fan in gates"):
  with members:
    - "computing majority with low fan in majority queries"
    - "super linear gate and super quadratic wire lower bounds for depth two and depth three threshold circuits"
    - "analysis of boolean functions"
    - "improved bounds for the randomized decision tree complexity of recursive majority"

Question: Please tell me which class the center node 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)