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: "on the synchronizing probability function and the triple rendezvous time for synchronizing automata"
  Abstract: Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping three states onto a single one. The second one is the synchronizing probability function of an automaton, a recently introduced tool which reinterprets the synchronizing phenomenon as a two-player game, and allows to obtain optimal strategies through a Linear Program. #R##N#Our contribution is twofold. First, by coupling two different novel approaches based on the synchronizing probability function and properties of linear programming, we obtain a new upper bound on the triple rendezvous time. Second, by exhibiting a family of counterexamples, we disprove a conjecture on the growth of the synchronizing probability function. We then suggest natural follow-ups towards Cernys conjecture.

Connected through hyperedge HE-1 (induced by source paper "cerny starke conjecture from the sixties of xx century"):
  with members:
    - "matrix approach to synchronizing automata"
    - "finding dfas with maximal shortest synchronizing word length"
    - "primitive sets of nonnegative matrices and synchronizing automata"
    - "a note on a recent attempt to improve the pin frankl bound"
    - "algebraic synchronization criterion and computing reset words"
    - "slowly synchronizing automata and digraphs"

Connected through hyperedge HE-2 (induced by source paper "matrix approach to synchronizing automata"):
  with members:
    - "improving the upper bound on the length of the shortest reset word"
    - "finding dfas with maximal shortest synchronizing word length"
    - "primitive sets of nonnegative matrices and synchronizing automata"
    - "a note on a recent attempt to improve the pin frankl bound"
    - "algebraic synchronization criterion and computing reset words"
    - "slowly synchronizing automata and digraphs"

Connected through hyperedge HE-3 (induced by source paper "on completely reachable automata and subset reachability"):
  with members:
    - "complexity of preimage problems for deterministic finite automata"
    - "improving the upper bound on the length of the shortest reset word"
    - "on the interplay between babai and v c ern y s conjectures"
    - "completely reachable automata"
    - "reachability of consensus and synchronizing automata"
    - "subset synchronization and careful synchronization of binary finite automata"
    - "subset synchronization of transitive automata"
    - "a note on a recent attempt to improve the pin frankl bound"

Connected through hyperedge HE-4 (induced by source paper "on the interplay between babai and v c ern y s conjectures"):
  with members:
    - "improving the upper bound on the length of the shortest reset word"
    - "primitive sets of nonnegative matrices and synchronizing automata"
    - "reachability of consensus and synchronizing automata"
    - "reset complexity of ideal languages"
    - "subset synchronization of transitive automata"
    - "preset distinguishing sequences and diameter of transformation semigroups"
    - "primitive digraphs with large exponents and slowly synchronizing automata"

Connected through hyperedge HE-5 (induced by source paper "reachability of consensus and synchronizing automata"):
  with members:
    - "efficient algorithms for the consensus decision problem"
    - "p l aying for synchronization"
    - "approximating the minimum length of synchronizing words is hard"
    - "the road coloring problem"

Connected through hyperedge HE-6 (induced by source paper "a note on a recent attempt to improve the pin frankl bound"):
  with members:
    - "modifying the upper bound on the length of minimal synchronizing word"

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.FL(Formal Languages and Automata Theory)