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 "almost settling the hardness of noncommutative determinant"):
  Abstract: In this paper, we study the complexity of computing the determinant of a matrix over a noncommutative algebra. In particular, we ask the question: "Over which algebras is the determinant easier to compute than the permanent?" Towards resolving this question, we show the following results for noncommutative determinant computation: [Hardness] Computing the determinant of an n x n matrix whose entries are themselves 2 x 2 matrices over any field of zero or odd characteristic is as hard as computing the permanent over the field. This extends the recent result of Arvind and Srinivasan, which required the entries to be matrices of dimension linear in n. [Easiness] The determinant of an n x n matrix whose entries are themselves d x d upper triangular matrices can be computed in poly(nd) time. Combining the above with the decomposition theorem for finite dimensional algebras (and in particular exploiting the simple structure of 2 x 2 matrix algebras), we can extend the above hardness and easiness statements to more general algebras as follows. Let A be a finite dimensional algebra over a finite field of odd characteristic with radical R(A). [Hardness] If the quotient A/R(A) is noncommutative, then computing the determinant over the algebra A is as hard as computing the permanent. [Easiness] If the quotient A/R(A) is commutative, and furthermore R(A) has nilpotency index d (i.e., d is the smallest integer such that R(A)d =0), then there exists a poly(nd)-time algorithm that computes determinants over the algebra A. In particular, for any constant dimensional algebra A over a finite field of odd characteristic, since the nilpotency index of R(A) is at most a constant, we have the following dichotomy theorem: if A/R(A) is commutative then efficient determinant computation is possible, and otherwise determinant is as hard as permanent.

Includes members:
  Member "on the hardness of the noncommutative determinant":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on explicit branching programs for the rectangular determinant and permanent polynomials")
  Member "approximating the permanent via nonabelian determinants":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the hardness of the noncommutative determinant")

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)