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 "boundaries of vp and vnp"):
  Abstract: One fundamental question in the context of the geometric complexity theory approach to the VP vs. VNP conjecture is whether VP = $\overline{\textrm{VP}}$, where VP is the class of families of polynomials that are of polynomial degree and can be computed by arithmetic circuits of polynomial size, and $\overline{\textrm{VP}}$ is the class of families of polynomials that are of polynomial degree and can be approximated infinitesimally closely by arithmetic circuits of polynomial size. The goal of this article is to study the conjecture in (Mulmuley, FOCS 2012) that $\overline{\textrm{VP}}$ is not contained in VP. #R##N#Towards that end, we introduce three degenerations of VP (i.e., sets of points in $\overline{\textrm{VP}}$), namely the stable degeneration Stable-VP, the Newton degeneration Newton-VP, and the p-definable one-parameter degeneration VP*. We also introduce analogous degenerations of VNP. We show that Stable-VP $\subseteq$ Newton-VP $\subseteq$ VP* $\subseteq$ VNP, and Stable-VNP = Newton-VNP = VNP* = VNP. The three notions of degenerations and the proof of this result shed light on the problem of separating $\overline{\textrm{VP}}$ from VP. #R##N#Although we do not yet construct explicit candidates for the polynomial families in $\overline{\textrm{VP}}\setminus$VP, we prove results which tell us where not to look for such families. Specifically, we demonstrate that the families in Newton-VP $\setminus$ VP based on semi-invariants of quivers would have to be non-generic by showing that, for many finite quivers (including some wild ones), any Newton degeneration of a generic semi-invariant can be computed by a circuit of polynomial size. We also show that the Newton degenerations of perfect matching Pfaffians, monotone arithmetic circuits over the reals, and Schur polynomials have polynomial-size circuits.

Includes members:
  Member "the complexity of factors of multivariate polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "algebraic branching programs border complexity and tangent spaces")
  Member "unifying known lower bounds via geometric complexity theory":
    also connected through other hyperedges:
      - Hyperedge HE-2 (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-3 (induced by source paper "a generalized sylvester gallai type theorem for quadratic polynomials")
  Member "deterministic polynomial time algorithms for matrix completion problems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")

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)