human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "a linear upper bound on the weisfeiler leman dimension of graphs of bounded genus"):
  with members:
    - "canonisation and definability for graphs of bounded rank width"
    - "a finite model theoretic view on propositional proof complexity"
    - "weisfeiler and leman go neural higher order graph neural networks"
    - "definable ellipsoid method sums of squares proofs and the isomorphism problem"
    - "the weisfeiler leman dimension of planar graphs is at most 3"
    - "on the combinatorial power of the weisfeiler lehman algorithm"
    - "semi supervised classification with graph convolutional networks"
    - "graph isomorphism in quasipolynomial time"

Connected through hyperedge HE-2 (induced by source paper "towards a practical k dimensional weisfeiler leman algorithm"):
  with members:
    - "a survey on graph kernels"
    - "provably powerful graph networks"
    - "faster kernels for graphs with continuous attributes via hashing"
    - "graph isomorphism in quasipolynomial time"
    - "graphs identified by logics with counting"
    - "tight lower and upper bounds for the complexity of canonical colour refinement"
    - "practical graph isomorphism ii"
    - "dimension reduction via colour refinement"

Connected through hyperedge HE-3 (induced by source paper "walk refinement walk logic and the iteration number of the weisfeiler leman algorithm"):
  with members:
    - "linear diophantine equations group csps and graph isomorphism"
    - "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps"
    - "the propagation depth of local consistency"

Connected through hyperedge HE-4 (induced by source paper "the weisfeiler leman dimension of planar graphs is at most 3"):
  with members:
    - "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps"
    - "tangled up in blue a survey on connectivity decompositions and tangles"
    - "graphs identified by logics with counting"
    - "dynamic complexity of planar 3 connected graph isomorphism"
    - "practical graph isomorphism ii"
    - "pebble games and linear equations"
    - "planar graphs logical complexity and parallel isomorphism tests"
    - "testing graph isomorphism in parallel by playing a game"

Connected through hyperedge HE-5 (induced by source paper "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps"):
  with members:
    - "graph isomorphism in quasipolynomial time"
    - "a generalized method for proving polynomial calculus degree lower bounds"
    - "universal covers color refinement and two variable counting logic lower bounds for the depth"
    - "the propagation depth of local consistency"
    - "pebble games proof complexity and time space trade offs"
    - "understanding space in proof complexity separations and trade offs via substitutions"

Question: Please tell me which class the center node 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)