VC-dimensions of nondeterministic finite automata for words of equal length
University of Hawai‘i at Mānoa（夏威夷大学马诺阿分校）
Bjørn Kjos-Hanssen, Clyde James Felix, Sun Young Kim, Ethan Lamb, Davin Takahashi
备注：
ISAIM 2020 (International Symposium on Artificial Intelligence and Mathematics), Fort Lauderdale, FL. January 6--8, 2020. Accepted for publication in Annals of Mathematics and Artificial Intelligence
Let $NFA_b(q)$ denote the set of languages accepted by nondeterministic finite automata with $q$ states over an alphabet with $b$ letters. Let $B_n$ denote the set of words of length $n$. We give a quadratic lower bound on the VC dimension of \[
NFA_2(q)\cap B_n = \{L\cap B_n \mid L \in NFA_2(q)\} \] as a function of $q$.
Next, the work of Gruber and Holzer (2007) gives an upper bound for the nondeterministic state complexity of finite languages contained in $B_n$, which we strengthen using our methods.
Finally, we give some theoretical and experimental results on the dependence on $n$ of the VC dimension and testing dimension of $NFA_2(q)\cap B_n$.
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University of Twente（特文特大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；University of Liverpool（利物浦大学）
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Universidade Federal do Vale do São Francisco（圣弗朗西斯科河谷联邦大学）；Universidade Federal do Rio Grande do Norte（北大河州联邦大学）
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