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 "jacobian hits circuits hitting sets lower bounds for depth d occur k formulas depth 3 transcendence degree k circuits"):
  Abstract: We present a single, common tool to strictly subsume all known cases of polynomial time blackbox polynomial identity testing (PIT) that have been hitherto solved using diverse tools and techniques. In particular, we show that polynomial time hitting-set generators for identity testing of the two seemingly different and well studied models - depth-3 circuits with bounded top fanin, and constant-depth constant-read multilinear formulas - can be constructed using one common algebraic-geometry theme: Jacobian captures algebraic independence. By exploiting the Jacobian, we design the first efficient hitting-set generators for broad generalizations of the above-mentioned models, namely: #R##N#(1) depth-3 (Sigma-Pi-Sigma) circuits with constant transcendence degree of the polynomials computed by the product gates (no bounded top fanin restriction), and (2) constant-depth constant-occur formulas (no multilinear restriction). #R##N#Constant-occur of a variable, as we define it, is a much more general concept than constant-read. Also, earlier work on the latter model assumed that the formula is multilinear. Thus, our work goes further beyond the results obtained by Saxena & Seshadhri (STOC 2011), Saraf & Volkovich (STOC 2011), Anderson et al. (CCC 2011), Beecken et al. (ICALP 2011) and Grenet et al. (FSTTCS 2011), and brings them under one unifying technique. #R##N#In addition, using the same Jacobian based approach, we prove exponential lower bounds for the immanant (which includes permanent and determinant) on the same depth-3 and depth-4 models for which we give efficient PIT algorithms. Our results reinforce the intimate connection between identity testing and lower bounds by exhibiting a concrete mathematical tool - the Jacobian - that is equally effective in solving both the problems on certain interesting and previously well-investigated (but not well understood) models of computation.

Includes members:
  Member "algebraic independence in positive characteristic a p adic calculus":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "algebraic dependencies and pspace algorithms in approximative complexity")
  Member "the limited power of powering polynomial identity testing and a depth four lower bound for the permanent":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "computing the multilinear factors of lacunary polynomials without heights")
  Member "algebraic independence and blackbox identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a generalized sylvester gallai type theorem for quadratic polynomials")
  Member "blackbox identity testing for bounded top fanin depth 3 circuits the field doesn t matter":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a generalized sylvester gallai type theorem for quadratic polynomials")
  Member "from sylvester gallai configurations to rank bounds improved black box identity test for depth 3 circuits":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "arithmetic circuits with locally low algebraic rank")
  Member "deterministic polynomial time algorithms for matrix completion problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "an almost optimal rank bound for depth 3 identities":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "succinct hitting sets and barriers to proving algebraic circuits lower bounds")

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)