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 "upper bounds on the quantifier depth for graph differentiation in first order logic"):
  Abstract: We show that on graphs with n vertices the 2-dimensional Weisfeiler-Leman algorithm requires at most O(n^2/log(n)) iterations to reach stabilization. This in particular shows that the previously best, trivial upper bound of O(n^2) is asymptotically not tight. In the logic setting this translates to the statement that if two graphs of size n can be distinguished by a formula in first order logic with counting with 3 variables (i.e., in C3) then they can also be distinguished by a C3-formula that has quantifier depth at most O(n^2/log(n)). #R##N#To prove the result we define a game between two players that enables us to decouple the causal dependencies between the processes happening simultaneously over several iterations of the algorithm. This allows us to treat large color classes and small color classes separately. As part of our proof we show that for graphs with bounded color class size, the number of iterations until stabilization is at most linear in the number of vertices. This also yields a corresponding statement in first order logic with counting. #R##N#Similar results can be obtained for the respective logic without counting quantifiers, i.e., for the logic L3.

Includes members:
  Member "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lifting with simple gadgets and applications to circuit and proof complexity")
  Member "graph isomorphism in quasipolynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hypergraph isomorphism for groups with restricted composition factors")
  Member "graphs identified by logics with counting":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "what graph neural networks cannot learn depth vs width")
  Member "tight lower and upper bounds for the complexity of canonical colour refinement":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "hypergraph isomorphism for groups with restricted composition factors")
  Member "universal covers color refinement and two variable counting logic lower bounds for the depth":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a linear upper bound on the weisfeiler leman dimension of graphs of bounded genus")
  Member "the propagation depth of local consistency":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "walk refinement walk logic and the iteration number of the weisfeiler leman algorithm")
  Member "practical graph isomorphism ii":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "hypergraph isomorphism for groups with restricted composition factors")
  Member "dimension reduction via colour refinement":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "towards a practical k dimensional weisfeiler leman algorithm")

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.LO(Logic in Computer Science)