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Deterministic blow-ups of minimal NFA's

Published online by Cambridge University Press:  18 October 2006

Galina Jirásková
Galina Jirásková*
Affiliation:
Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovakia; jiraskov@saske.sk
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Abstract

The paper treats the question whether there always exists a minimal nondeterministic finite automaton of n states whose equivalent minimal deterministic finite automaton has α states for any integers n and α with n ≤ α ≤ 2n .Partial answers to this question were given by Iwama, Kambayashi, and Takaki (2000) and by Iwama, Matsuura, and Paterson (2003). In the present paper, the question is completely solved by presenting appropriate automata for all values of n and α. However, in order to give an explicit construction of the automata, we increase the input alphabet to exponential sizes. Then we prove that 2n letters would be sufficient but we describe the related automata only implicitly. In the last section, we investigate the above question for automata over binary and unary alphabets.

Keywords

Regular languagesdeterministic finite automatanondeterministic finite automatastate complexity.

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