Deterministic blow-ups of minimal NFA's

Galina Jirásková

RAIRO - Theoretical Informatics and Applications (2006)

  • Volume: 40, Issue: 3, page 485-499
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Jirásková, Galina. "Deterministic blow-ups of minimal NFA's." RAIRO - Theoretical Informatics and Applications 40.3 (2006): 485-499. <http://eudml.org/doc/249681>.

@article{Jirásková2006,
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. },
author = {Jirásková, Galina},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Regular languages; deterministic finite automata; nondeterministic finite automata; state complexity.; regular languages; state complexity},
language = {eng},
month = {10},
number = {3},
pages = {485-499},
publisher = {EDP Sciences},
title = {Deterministic blow-ups of minimal NFA's},
url = {http://eudml.org/doc/249681},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Jirásková, Galina
TI - Deterministic blow-ups of minimal NFA's
JO - RAIRO - Theoretical Informatics and Applications
DA - 2006/10//
PB - EDP Sciences
VL - 40
IS - 3
SP - 485
EP - 499
AB - 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.
LA - eng
KW - Regular languages; deterministic finite automata; nondeterministic finite automata; state complexity.; regular languages; state complexity
UR - http://eudml.org/doc/249681
ER -

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