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 "the complexity of counting edge colorings and a dichotomy for some higher domain holant problems"):
  Abstract: We show that an effective version of Siegel's Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems, denoted by Holant(f), are defined by a symmetric ternary function f that is invariant under any permutation of the k >= 3 domain elements. We prove that Holant(f) exhibits a complexity dichotomy. This dichotomy holds even when restricted to planar graphs. A special case of this result is that counting edge k-colorings is #P-hard over planar 3-regular graphs for k >= 3. In fact, we prove that counting edge k-colorings is #P-hard over planar r-regular graphs for all k >= r >= 3. The problem is polynomial-time computable in all other parameter settings. The proof of the dichotomy theorem for Holant(f) depends on the fact that a specific polynomial p(x,y) has an explicitly listed finite set of integer solutions, and the determination of the Galois groups of some specific polynomials. In the process, we also encounter the Tutte polynomial, medial graphs, Eulerian partitions, Puiseux series, and a certain lattice condition on the (logarithm of) the roots of polynomials.

Includes members:
  Member "the complexity of planar boolean csp with complex weights":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "complexity of counting weighted eulerian orientations with ars")
  Member "dichotomy for holant problems with a function on domain size 3":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "base collapse of holographic algorithms")
  Member "complexity of counting csp with complex weights":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "optimal polynomial time compression for boolean max csp")
  Member "gadgets and anti gadgets leading to a complexity dichotomy":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a holant dichotomy is the fkt algorithm universal")
  Member "on tractable exponential sums":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "stabilizer circuits quadratic forms and computing matrix rank")
  Member "holant problems for regular graphs with complex edge functions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the complexity of planar boolean csp with complex weights")
  Member "from holant to csp and back dichotomy for holant c problems":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "holant clones and the approximability of conservative holant problems")
  Member "graph homomorphisms with complex values a dichotomy theorem":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "a dichotomy for bounded degree graph homomorphisms with nonnegative weights")

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)