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 "a dichotomy for bounded degree graph homomorphisms with nonnegative weights"):
  Abstract: We consider the complexity of counting weighted graph homomorphisms defined by a symmetric matrix $A$. Each symmetric matrix $A$ defines a graph homomorphism function $Z_A(\cdot)$, also known as the partition function. Dyer and Greenhill [10] established a complexity dichotomy of $Z_A(\cdot)$ for symmetric $\{0, 1\}$-matrices $A$, and they further proved that its #P-hardness part also holds for bounded degree graphs. Bulatov and Grohe [4] extended the Dyer-Greenhill dichotomy to nonnegative symmetric matrices $A$. However, their hardness proof requires graphs of arbitrarily large degree, and whether the bounded degree part of the Dyer-Greenhill dichotomy can be extended has been an open problem for 15 years. We resolve this open problem and prove that for nonnegative symmetric $A$, either $Z_A(G)$ is in polynomial time for all graphs $G$, or it is #P-hard for bounded degree (and simple) graphs $G$. We further extend the complexity dichotomy to include nonnegative vertex weights. Additionally, we prove that the #P-hardness part of the dichotomy by Goldberg et al. [12] for $Z_A(\cdot)$ also holds for simple graphs, where $A$ is any real symmetric matrix.

Includes members:
  Member "algorithmic pirogov sinai theory":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "correlation decay up to uniqueness in spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "counting homomorphisms and partition functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "perfect matchings rank of connection tensors and graph homomorphisms")
  Member "computational transition at the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "a decidable dichotomy theorem on directed graph homomorphisms with non negative weights":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on a theorem of lovasz that hom cdot h determines the isomorhphism type of h")
  Member "the complexity of partition functions on hermitian matrices":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the complexity of planar boolean csp with complex weights")
  Member "graph homomorphisms with complex values a dichotomy theorem":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "perfect matchings rank of connection tensors and graph homomorphisms")
  Member "a complexity dichotomy for partition functions with mixed signs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "perfect matchings rank of connection tensors and graph homomorphisms")

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)