VC-dimensions of nondeterministic finite automata for words of equal length

01/07/2020

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by   Bjørn Kjos-Hanssen, et al.

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Ishigami and Tani studied VC-dimensions of deterministic finite automata. We obtain analogous results for the nondeterministic case by extending a result of Champarnaud and Pin, who proved that the maximal deterministic state complexity of a set of binary words of length n is ∑_i=0^nmin(2^i,2^2^n-i-1). We show that for the nondeterministic case, if we fully restrict attention to words of length n, then we at most need the strictly increasing initial terms in this sum.