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 "proof complexity lower bounds from algebraic circuit complexity"):
  Abstract: We give upper and lower bounds on the power of subsystems of the Ideal Proof System (IPS), the algebraic proof system recently proposed by Grochow and Pitassi [26], where the circuits comprising the proof come from various restricted algebraic circuit classes. This mimics an established research direction in the boolean setting for subsystems of Extended Frege proofs whose lines are circuits from restricted boolean circuit classes. Essentially all of the subsystems considered in this paper can simulate the well-studied Nullstellensatz proof system, and prior to this work there were no known lower bounds when measuring proof size by the algebraic complexity of the polynomials (except with respect to degree, or to sparsity).#R##N##R##N#Our main contributions are two general methods of converting certain algebraic lower bounds into proof complexity ones. Both require stronger arithmetic lower bounds than common, which should hold not for a specific polynomial but for a whole family defined by it. These may be likened to some of the methods by which Boolean circuit lower bounds are turned into related proof-complexity ones, especially the "feasible interpolation" technique. We establish algebraic lower bounds of these forms for several explicit polynomials, against a variety of classes, and infer the relevant proof complexity bounds. These yield separations between IPS subsystems, which we complement by simulations to create a partial structure theory for IPS systems.#R##N##R##N#Our first method is a functional lower bound, a notion of Grigoriev and Razborov [25], which is a function [EQUATION] {0, 1}n → F such that any polynomial f agreeing with [EQUATION] on the boolean cube requires large algebraic circuit complexity. We develop functional lower bounds for a variety of circuit classes (sparse polynomials, depth-3 powering formulas, read-once algebraic branching programs and multilinear formulas) where [EQUATION] equals [EQUATION] for a constant-degree polynomial p depending on the relevant circuit class. We believe these lower bounds are of independent interest in algebraic complexity, and show that they also imply lower bounds for the size of the corresponding IPS refutations for proving that the relevant polynomial p is non-zero over the boolean cube. In particular, we show super-polynomial lower bounds for refuting variants of the subset-sum axioms in these IPS subsystems.#R##N##R##N#Our second method is to give lower bounds for multiples, that is, to give explicit polynomials whose all (non-zero) multiples require large algebraic circuit complexity. By extending known techniques, we give lower bounds for multiples for various restricted circuit classes such sparse polynomials, sums of powers of low-degree polynomials, and roABPs. These results are of independent interest, as we argue that lower bounds for multiples is the correct notion for instantiating the algebraic hardness versus randomness paradigm of Kabanets and Impagliazzo [31]. Further, we show how such lower bounds for multiples extend to lower bounds for refutations in the corresponding IPS subsystem.

Includes members:
  Member "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "symmetric arithmetic circuits")
  Member "an exponential lower bound for homogeneous depth 5 circuits over finite fields":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing")
  Member "identity testing and lower bounds for read k oblivious algebraic branching programs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "algebraic branching programs border complexity and tangent spaces")
  Member "circuit complexity proof complexity and polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "search problems in algebraic complexity gct and hardness of generator for invariant rings")
  Member "subexponential size hitting sets for bounded depth multilinear formulas":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a note on polynomial identity testing for depth 3 circuits")
  Member "hitting sets for roabp and sum of set multilinear circuits":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "lower bounds for matrix factorization")
  Member "deterministic identity testing for sum of read once oblivious arithmetic branching programs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "succinct hitting sets and barriers to proving algebraic circuits lower bounds")
  Member "explicit noether normalization for simultaneous conjugation via polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "a generalized sylvester gallai type theorem for quadratic polynomials")

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)