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 "infinite games specified by 2 tape automata"):
  Abstract: We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. Then we prove that winning strategies, when they exist, can be very complex, i.e. highly non-effective, in these games. We prove the same results for Gale-Stewart games with winning sets accepted by real-time 1-counter B\"uchi automata, then extending previous results obtained about these games. Then we consider the strenghs of determinacy for these games, and we prove that there is a transfinite sequence of 2-tape B\"uchi automata (respectively, of real-time 1-counter B\"uchi automata) $A_\alpha$, indexed by recursive ordinals, such that the games $G(L(A_\alpha))$ have strictly increasing strenghs of determinacy. Moreover there is a 2-tape B\"uchi automaton (respectively, a real-time 1-counter B\"uchi automaton) B such that the determinacy of G(L(B)) is equivalent to the (effective) analytic determinacy and thus has the maximal strength of determinacy. We show also that the determinacy of Wadge games between two players in charge of infinitary rational relations accepted by 2-tape B\"uchi automata is equivalent to the (effective) analytic determinacy, and thus not provable in ZFC.

Includes members:
  Member "the determinacy of context free games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an upper bound on the complexity of recognizable tree languages")
  Member "highly undecidable problems for infinite computations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "three applications to rational relations of the high undecidability of the infinite post correspondence problem in a regular omega language")
  Member "the complexity of infinite computations in models of set theory":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the determinacy of context free games")
  Member "wadge degrees of infinitary rational relations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "topological complexity of context free omega languages a survey")
  Member "borel ranks and wadge degrees of context free omega languages":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "three applications to rational relations of the high undecidability of the infinite post correspondence problem in a regular omega language")

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)