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: "the number of languages with maximum state complexity"
  Abstract: Champarnaud and Pin (1989) found that the minimal deterministic automaton of a language $L\subset\Sigma^n$, where $\Sigma=\{0,1\}$, has at most \[ #R##N#\sum_{i=0}^n \min(2^i, 2^{2^{n-i}}-1) \] states, and for each $n$ there exists $L$ attaining this bound. C\^{a}mpeanu and Ho (2004) have shown more generally that the tight upper bound for $\Sigma$ of cardinality $k$ and for complete automata is \[ #R##N#\frac{k^r-1}{k-1} + \sum_{j=0}^{n-r}(2^{k^j}-1) + 1 \] where $r=\min\{m:k^m\ge 2^{k^{n-m}}-1\}$. (In these results, requiring totality of the transition function adds 1 to the state count.) C\^{a}mpeanu and Ho's result can be viewed as concerning functions $f:[k]^n\to [2]$ where $[k]=\{0,\dots,k-1\}$ is a set of cardinality $k$. We generalize their result to arbitrary function $f:[k]^n\to [c]$ where $c$ is a positive integer. Let $O_i$ be the number of functions from $[b^{i}]$ to $[c^{b^{n-i}}]$ that are onto $[c^{b^{n-i}}-1]$. C\^ampeanu and Ho stated that it is very difficult to determine the number of maximum-complexity languages. Here we show that it is equal to $O_i$, for the least $i$ such that $O_i>0$. For monotone languages a tightness result seems harder to obtain. However, we show that the following upper bound is attained for all $n\le 10$. \[ #R##N#\sum_{i=0}^n \min(2^i, M(n-i)-1), \] where $M(k)$ is the $k$th Dedekind number.

Connected through hyperedge HE-1 (induced by source paper "vc dimensions of nondeterministic finite automata for words of equal length"):
  with members:
    - "nondeterministic automatic complexity of overlap free and almost square free words"

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)