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 "on algebraic branching programs of small width"):
  Abstract: In 1979 Valiant showed that the complexity class VP_e of families with polynomially bounded formula size is contained in the class VP_s of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes we study the topological closure VP_e-bar, i.e. the class of polynomials that can be approximated arbitrarily closely by polynomials in VP_e. We describe VP_e-bar with a strikingly simple complete polynomial (in characteristic different from 2) whose recursive definition is similar to the Fibonacci numbers. Further understanding this polynomial seems to be a promising route to new formula lower bounds. #R##N#Our methods are rooted in the study of ABPs of small constant width. In 1992 Ben-Or and Cleve showed that formula size is polynomially equivalent to width-3 ABP size. We extend their result (in characteristic different from 2) by showing that approximate formula size is polynomially equivalent to approximate width-2 ABP size. This is surprising because in 2011 Allender and Wang gave explicit polynomials that cannot be computed by width-2 ABPs at all! The details of our construction lead to the aforementioned characterization of VP_e-bar. #R##N#As a natural continuation of this work we prove that the class VNP can be described as the class of families that admit a hypercube summation of polynomially bounded dimension over a product of polynomially many affine linear forms. This gives the first separations of algebraic complexity classes from their nondeterministic analogs.

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 "succinct hitting sets and barriers to proving algebraic circuits lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "implementing geometric complexity theory on the separation of orbit closures via symmetries")
  Member "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "symmetric arithmetic circuits")
  Member "no occurrence obstructions in geometric complexity theory":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the computational complexity of plethysm coefficients")
  Member "a 2n 2 log n 1 lower bound for the border rank of matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "matrix multiplication algorithms from group orbits")
  Member "boundaries of vp and vnp":
    also connected through other hyperedges:
      - Hyperedge HE-6 (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-7 (induced by source paper "succinct hitting sets and barriers to proving algebraic circuits lower bounds")
  Member "a lower bound for the determinantal complexity of a hypersurface":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "algebraic branching programs border complexity and tangent spaces")

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)