Magic Numbers and Ternary Alphabet

Authors:
Galina Jirásková
Affiliations:
Mathematical Institute, Slovak Academy of Sciences, Košice, Slovakia 040 01
Venue:
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Year:
2009

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Abstract

A number 驴, 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 驴 states. We show that in the case of a ternary alphabet, there are no magic numbers. For all n and 驴 satisfying that $n \leqslant \alpha \leqslant 2^n$, we describe an n-state nondeterministic automaton with a three-letter input alphabet that needs 驴 deterministic states.