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 "walk refinement walk logic and the iteration number of the weisfeiler leman algorithm"):
  Abstract: We show that the 2-dimensional Weisfeiler-Leman algorithm stabilizes n-vertex graphs after at most O(n log n) iterations. This implies that if such graphs are distinguishable in 3-variable first order logic with counting, then they can also be distinguished in this logic by a formula of quantifier depth at most O(n log n). #R##N#For this we exploit a new refinement based on counting walks and argue that its iteration number differs from the classic Weisfeiler-Leman refinement by at most a logarithmic factor. We then prove matching linear upper and lower bounds on the number of iterations of the walk refinement. This is achieved with an algebraic approach by exploiting properties of semisimple matrix algebras. We also define a walk logic and a bijective walk pebble game that precisely correspond to the new walk refinement.

Includes members:
  Member "linear diophantine equations group csps and graph isomorphism":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a finite model theoretic view on propositional proof complexity")
  Member "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lifting with simple gadgets and applications to circuit and proof complexity")
  Member "upper bounds on the quantifier depth for graph differentiation in first order logic":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (induced by source paper "upper bounds on the quantifier depth for graph differentiation in first order logic")

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)