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 "lower bounds for multilinear bounded order abps"):
  Abstract: Proving super-polynomial size lower bounds for syntactic multilinear Algebraic Branching Programs(smABPs) computing an explicit polynomial is a challenging problem in Algebraic Complexity Theory. The order in which variables in $\{x_1,\ldots,x_n\}$ appear along source to sink paths in any smABP can be viewed as a permutation in $S_n$. In this article, we consider the following special classes of smABPs where the order of occurrence of variables along a source to sink path is restricted: #R##N#Strict circular-interval ABPs: For every subprogram the index set of variables occurring in it is contained in some circular interval of $\{1,\ldots,n\}$. #R##N#L-ordered ABPs: There is a set of L permutations of variables such that every source to sink path in the ABP reads variables in one of the L orders. #R##N#We prove exponential lower bound for the size of a strict circular-interval ABP computing an explicit n-variate multilinear polynomial in VP. For the same polynomial, we show that any sum of L-ordered ABPs of small size will require exponential ($2^{n^{\Omega(1)}}$) many summands, when $L \leq 2^{n^{1/2-\epsilon}}, \epsilon>0$. At the heart of above lower bound arguments is a new decomposition theorem for smABPs: We show that any polynomial computable by an smABP of size S can be written as a sum of O(S) many multilinear polynomials where each summand is a product of two polynomials in at most 2n/3 variables computable by smABPs. As a corollary, we obtain a low bottom fan-in version of the depth reduction by Tavenas [MFCS 2013] in the case of smABPs. In particular, we show that a polynomial having size S smABPs can be expressed as a sum of products of multilinear polynomials on $O(\sqrt{n})$ variables, where the total number of summands is bounded by $2^{O(\sqrt{n}\log n \log S)}$. Additionally, we show that L-ordered ABPs can be transformed into L-pass smABPs with a polynomial blowup in size.

Includes members:
  Member "small depth multilinear formula lower bounds for iterated matrix multiplication with applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new exponential size lower bounds against depth four circuits of bounded individual degree")
  Member "some lower bound results for set multilinear arithmetic computations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lower bounds for special cases of syntactic multilinear abps")
  Member "improved bounds for reduction to depth 4 and depth 3":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lower bounds for matrix factorization")

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)