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 expressibility of functions on the boolean domain with applications to counting csps"):
  Abstract: An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base relations. Post's lattice gives a complete classification of all Boolean relational clones, and this has been used to classify the computational difficulty of CSPs. Motivated by a desire to understand the computational complexity of (weighted) counting CSPs, we develop an analogous notion of functional clones and study the landscape of these clones. One of these clones is the collection of log-supermodular (lsm) functions, which turns out to play a significant role in classifying counting CSPs. In the conservative case (where all nonnegative unary functions are available), we show that there are no functional clones lying strictly between the clone of lsm functions and the total clone (containing all functions). Thus, any counting CSP that contains a single nontrivial non-lsm function is computationally as hard to approximate as any problem in #P. Furthermore, we show that any nontrivial functional clone (in a sense that will be made precise) contains the binary function “implies”. As a consequence, in the conservative case, all nontrivial counting CSPs are as hard to approximate as #BIS, the problem of counting independent sets in a bipartite graph. Given the complexity-theoretic results, it is natural to ask whether the “implies” clone is equivalent to the clone of lsm functions. We use the Mobius transform and the Fourier transform to show that these clones coincide precisely up to arity 3. It is an intriguing open question whether the lsm clone is finitely generated. Finally, we investigate functional clones in which only restricted classes of unary functions are available.

Includes members:
  Member "the complexity of conservative valued csps":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "representing fitness landscapes by valued constraints to understand the complexity of local search")
  Member "approximating the tutte polynomial of a binary matroid and other related combinatorial polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "log concave polynomials ii high dimensional walks and an fpras for counting bases of a matroid")
  Member "the complexity of weighted and unweighted csp":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "complexity of counting weighted eulerian orientations with ars")
  Member "the complexity of approximately counting stable matchings":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "algorithms for bis hard problems on expander graphs")
  Member "approximating the partition function of the ferromagnetic potts model":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "lsm is not generated by binary functions":
    also connected through other hyperedges:
      (none)
  Member "approximate counting for complex weighted boolean constraint satisfaction problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "holant clones and the approximability of conservative holant problems")
  Member "the expressive power of binary submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "binarisation for valued constraint satisfaction problems")

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)