Magic Numbers and Ternary Alphabet

A number ?, in the range from n to 2 n , is magic for n with respect to a given alphabet size s, if there is no minimal nondeterministic finite automaton of n states and s input letters whose equivalent minimal deterministic finite automaton has ? states. We show that in the case of a ternary alphabet, there are no magic numbers. For all n and ? satisfying that $n \leqslant \alpha \leqslant 2^n$, we describe an n-state nondeterministic automaton with a three-letter input alphabet that needs ? deterministic states.

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