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: "structure theorem and strict alternation hierarchy for fo2 on words"
  Abstract: It is well-known that every first-order property on words is expressible#N#using at most three variables. The subclass of properties expressible with only#N#two variables is also quite interesting and well-studied. We prove precise#N#structure theorems that characterize the exact expressive power of first-order#N#logic with two variables on words. Our results apply to both the case with and#N#without a successor relation. For both languages, our structure theorems show#N#exactly what is expressible using a given quantifier depth, n, and using m#N#blocks of alternating quantifiers, for any m \leq n. Using these#N#characterizations, we prove, among other results, that there is a strict#N#hierarchy of alternating quantifiers for both languages. The question whether#N#there was such a hierarchy had been completely open. As another consequence of#N#our structural results, we show that satisfiability for first-order logic with#N#two variables without successor, which is NEXP-complete in general, becomes#N#NP-complete once we only consider alphabets of a bounded size.

Connected through hyperedge HE-1 (induced by source paper "two variable logics with some betweenness relations expressiveness satisfiability and membership"):
  with members:
    - "going higher in the first order quantifier alternation hierarchy on words"

Connected through hyperedge HE-2 (induced by source paper "the word problem for omega terms over the trotter weil hierarchy"):
  with members:
    - "the separation problem for regular languages by piecewise testable languages"
    - "separating regular languages by piecewise testable and unambiguous languages"
    - "ehrenfeucht fraisse games on omega terms"
    - "the join levels of the trotter weil hierarchy are decidable"
    - "on logical hierarchies withinfoâ definable languages"
    - "the fo2 alternation hierarchy is decidable"
    - "representations of stream processors using nested fixed points"

Connected through hyperedge HE-3 (induced by source paper "testing simon s congruence"):
  with members:
    - "on the index of simon s congruence for piecewise testability"
    - "alternating towers and piecewise testable separators"

Connected through hyperedge HE-4 (induced by source paper "finite degree predicates and two variable first order logic"):
  with members:
    - "an effective characterization of the alternation hierarchy in two variable logic"
    - "non definability of languages by generalized first order formulas over n"

Connected through hyperedge HE-5 (induced by source paper "from algebra to logic there and back again the story of a hierarchy"):
  with members:
    - "essential convexity and complexity of semi algebraic constraints"
    - "an effective characterization of the alternation hierarchy in two variable logic"
    - "the fo2 alternation hierarchy is decidable"
    - "representations of stream processors using nested fixed points"

Connected through hyperedge HE-6 (induced by source paper "deterministic logics for ul"):
  with members:
    - "rankers over infinite words"

Connected through hyperedge HE-7 (induced by source paper "the fo2 alternation hierarchy is decidable"):
  with members:
    - "lattices of logical fragments over words"
    - "the join levels of the trotter weil hierarchy are decidable"
    - "languages of dot depth one over infinite words"
    - "an introduction to finite automata and their connection to logic"
    - "on fo 2 quantifier alternation over words"
    - "logic meets algebra the case of regular languages"

Connected through hyperedge HE-8 (induced by source paper "quantifier alternation in two variable first order logic with successor is decidable"):
  with members:
    - "lattices of logical fragments over words"
    - "the join levels of the trotter weil hierarchy are decidable"
    - "the fo2 alternation hierarchy is decidable"
    - "around dot depth one"

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)