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\iteman{io-port 05215379}
\itemau{Jir\'asek, Jozef; Jir\'askov\'a, Galina; Szabari, Alexander}
\itemti{Deterministic blow-ups of minimal nondeterministic finite automata over a fixed alphabet.}
\itemso{Harju, Tero (ed.) et al., Developments in language theory. 11th international conference, DLT 2007, Turku, Finland, July 3--6, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73207-5/pbk). Lecture Notes in Computer Science 4588, 254-265 (2007).}
\itemab
Summary: We show that for all integers $n$ and $\alpha $ such that $n \leqslant \alpha \leqslant 2^n$ there exists a minimal nondeterministic finite automaton of $n$ states with a four-letter input alphabet whose equivalent minimal deterministic finite automaton has exactly $\alpha $ states. It follows that in the case of a four-letter alphabet, there are no ``magic numbers'', i.e., holes in the hierarchy. This improves a similar result obtained by Geffert for a growing alphabet of size $n + 2$.
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\itemli{doi:10.1007/978-3-540-73208-2\_25}
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