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 complexity of infinite computations in models of set theory"):
  Abstract: We prove the following surprising result: there exist a 1-counter Buchi automaton A and a 2-tape Buchi automaton B such that : (1) There is a model $V_1$ of ZFC in which the omega-language $L(A)$ and the infinitary rational relation $L(B)$ are ${\bf \Pi}_2^0$-sets, and (2) There is a model $V_2$ of ZFC in which the omega-language $L(A)$ and the infinitary rational relation $L(B)$ are analytic but non Borel sets. This shows that the topological complexity of an omega-language accepted by a 1-counter Buchi automaton or of an infinitary rational relation accepted by a 2-tape Buchi automaton is not determined by the axiomatic system ZFC. We show that a similar result holds for the class of languages of infinite pictures which are recognized by Buchi tiling systems. We infer from the proof of the above results an improvement of the lower bound of some decision problems recently studied in previous papers [Fin09a, Fin09b].

Includes members:
  Member "borel hierarchy and omega context free languages":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the determinacy of context free games")
  Member "highly undecidable problems for infinite computations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "infinite games specified by 2 tape automata")
  Member "on recognizable languages of infinite pictures":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "highly undecidable problems for infinite computations")
  Member "topological complexity of context free omega languages a survey":
    also connected through other hyperedges:
      (none)
  Member "highly undecidable problems about recognizability by tiling systems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "highly undecidable problems for infinite computations")
  Member "borel ranks and wadge degrees of context free omega languages":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "infinite games specified by 2 tape automata")

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)