DETERMINISTIC BLOW-UPS OF MINIMAL NONDETERMINISTIC FINITE AUTOMATA OVER A FIXED ALPHABET

Abstract

We show that for all integers n and α such that n ⩽ α ⩽ 2n, there exists a minimal nondeterministic finite automaton of n states with a four-letter input alphabet whose equivalent minimal deterministic finite automaton has exactly α states. It follows that in the case of a four-letter alphabet, there are no "magic numbers", i.e., the holes in the hierarchy. This improves a similar result obtained by Geffert for a growing alphabet of size n + 2.