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 "lower bounds for synchronizing word lengths in partial automata"):
  Abstract: It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 7$, without bounds on the number of symbols. #R##N#For PFAs (partial automata) on $\leq 7$ states we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n \geq 4$. Where DFAs with long synchronization typically have very few symbols, for PFAs we observe that more symbols may increase the synchronizing word length. For PFAs on $\leq 9$ states and two symbols we investigate all occurring synchronizing word lengths. #R##N#We give series of PFAs on two and three symbols, reaching the maximal possible length for some small values of $n$. For $n=6,7,8,9$, the construction on two symbols is the unique one reaching the maximal length. For both series the growth is faster than $(n-1)^2$, although still quadratic. #R##N#Based on string rewriting, for arbitrary size we construct a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation. Both PFAs are transitive. #R##N#Finally, we show that exponential lengths are even possible with just one single undefined transition, again with transitive constructions.

Includes members:
  Member "finding dfas with maximal shortest synchronizing word length":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "cerny starke conjecture from the sixties of xx century")
  Member "primitive sets of nonnegative matrices and synchronizing automata":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "cerny starke conjecture from the sixties of xx century")
  Member "experiments with synchronizing automata":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a linear bound on the k rendezvous time for primitive sets of nz matrices")
  Member "subset synchronization and careful synchronization of binary finite automata":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on completely reachable automata and subset reachability")
  Member "primitive digraphs with large exponents and slowly synchronizing automata":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "optimal synchronization of partial deterministic finite 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.FL(Formal Languages and Automata Theory)