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 "lifting with simple gadgets and applications to circuit and proof complexity"):
  Abstract: We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to monotone span program size by Pitassi and Robere (2018) so that it works for any gadget with high enough rank, in particular, for useful gadgets such as equality and greater-than. We apply our generalized theorem to solve two open problems: #R##N#* We present the first result that demonstrates a separation in proof power for cutting planes with unbounded versus polynomially bounded coefficients. Specifically, we exhibit CNF formulas that can be refuted in quadratic length and constant line space in cutting planes with unbounded coefficients, but for which there are no refutations in subexponential length and subpolynomial line space if coefficients are restricted to be of polynomial magnitude. #R##N#* We give the first explicit separation between monotone Boolean formulas and monotone real formulas. Specifically, we give an explicit family of functions that can be computed with monotone real formulas of nearly linear size but require monotone Boolean formulas of exponential size. Previously only a non-explicit separation was known. #R##N#An important technical ingredient, which may be of independent interest, is that we show that the Nullstellensatz degree of refuting the pebbling formula over a DAG G over any field coincides exactly with the reversible pebbling price of G. In particular, this implies that the standard decision tree complexity and the parity decision tree complexity of the corresponding falsified clause search problem are equal.

Includes members:
  Member "extension complexity of independent set polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "quasi popular matchings optimality and extended formulations")
  Member "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "walk refinement walk logic and the iteration number of the weisfeiler leman algorithm")
  Member "approximating rectangles by juntas and weakly exponential lower bounds for lp relaxations of csps":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "list decodable subspace recovery")
  Member "space proof complexity for random 3 cnfs":
    also connected through other hyperedges:
      (none)
  Member "lower bounds on the size of semidefinite programming relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "quantum inspired classical sublinear time algorithm for solving low rank semidefinite programming via sampling approaches")
  Member "communication lower bounds via critical block sensitivity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "complexity theory game theory and economics the barbados lectures")

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)