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 "hardness amplification in proof complexity"):
  Abstract: We present a general method for converting any family of unsatisfiable CNF formulas that is hard for one of the simplest proof systems, tree resolution, into formulas that require large rank in any proof system that manipulates polynomials or polynomial threshold functions of degree at most k (known as Th(k) proofs). Such systems include Lovasz-Schrijver and Cutting Planes proof systems as well as their high degree analogues. #R##N#These are based on analyzing two new proof systems, denoted by T^cc(k) and R^cc(k). The proof lines of T^cc(k) are arbitrary Boolean functions, each of which can be evaluated by an efficient k-party randomized communication protocol. They include Th{k-1} proofs as a special case. R^cc(k) proofs are stronger and only require that each inference be locally checkable by an efficient k-party randomized communication protocol. #R##N#Our main results are the following: #R##N#(1) When k is O(loglogn), for any unsatisfiable CNF formula F requiring resolution rank r, there is a related CNF formula G=Lift_k(F) requiring refutation rank r^Omega(1/k) log^O(1) n in all R^cc(k) systems. #R##N#(2) There are strict hierarchies for T^cc(k) and R^cc(k) systems with respect to k when k is O(loglogn in that there are unsatisfiable CNF formulas requiring large rank R^cc(k) refutations but having log^O(1) n rank Th(k) refutations. #R##N#(3) When k is O(loglogn) there are 2^(n^Omega(1/k)) lower bounds on the size of tree-like T^cc(k) refutations for large classes of lifted CNF formulas. #R##N#(4) A general method for producing integrality gaps for low rank R^cc(2) inference (and hence Cutting Planes and Th(1) inference) based on related gaps for low rank resolution. These gaps are optimal for MAX-2t-SAT.

Includes members:
  Member "the pattern matrix method journal version":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "improved bounds on fourier entropy and min entropy")
  Member "multiparty communication complexity of disjointness":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a nearly optimal lower bound on the approximate degree of ac 0")
  Member "disjointness is hard in the multi party number on the forehead model":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "hardness amplification and the approximate degree of constant depth circuits")

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)