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3VC-dimensions of nondeterministic finite automata for words of equal length
Abstract
Let denote the set of languages accepted by nondeterministic finite automata with states over an alphabet with letters. Let denote the set of words of length . 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 . Next, the work of Gruber and Holzer (2007) gives an upper bound for the nondeterministic state complexity of finite languages contained in , which we strengthen using our methods. Finally, we give some theoretical and experimental results on the dependence on of the VC dimension and testing dimension of .
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