The paper treats the question whether there always exists a minimal nondeterministic finite automaton of states whose equivalent minimal deterministic finite automaton has states for any integers and with 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 and . However, in order to give an explicit construction of the automata, we increase the input alphabet to exponential sizes. Then we prove that 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.
Mots clés : regular languages, deterministic finite automata, nondeterministic finite automata, state complexity
@article{ITA_2006__40_3_485_0, author = {Jir\'askov\'a, Galina}, title = {Deterministic blow-ups of minimal {NFA's}}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {485--499}, publisher = {EDP-Sciences}, volume = {40}, number = {3}, year = {2006}, doi = {10.1051/ita:2006032}, zbl = {1110.68064}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2006032/} }
TY - JOUR AU - Jirásková, Galina TI - Deterministic blow-ups of minimal NFA's JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 485 EP - 499 VL - 40 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2006032/ DO - 10.1051/ita:2006032 LA - en ID - ITA_2006__40_3_485_0 ER -
%0 Journal Article %A Jirásková, Galina %T Deterministic blow-ups of minimal NFA's %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 485-499 %V 40 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2006032/ %R 10.1051/ita:2006032 %G en %F ITA_2006__40_3_485_0
Jirásková, Galina. Deterministic blow-ups of minimal NFA's. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 485-499. doi : 10.1051/ita:2006032. http://www.numdam.org/articles/10.1051/ita:2006032/
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