Conversion of regular expressions into realtime automata

Geffert, Viliam; Ištoňová, L'ubomíra

doi:10.1051/ita:2006036

Geffert, Viliam ; Ištoňová, L'ubomíra

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 4, pp. 611-629.

Résumé

We consider conversions of regular expressions into $k$ -realtime finite state automata, i.e., automata in which the number of consecutive uses of $ε$ -transitions, along any computation path, is bounded by a fixed constant $k$ . For $2$ -realtime automata, i.e., for automata that cannot change the state, without reading an input symbol, more than two times in a row, we show that the conversion of a regular expression into such an automaton produces only $O (n)$ states, $O (n log n)$ $ε$ -transitions, and $O (n)$ alphabet-transitions. We also show how to easily transform these $2$ -realtime machines into $1$ -realtime automata, still with only $O (n log n)$ edges. These results contrast with the known lower bound $Ω (n {(log n)}^{2} / log log n)$ , holding for $0$ -realtime automata, i.e., for automata with no $ε$ -transitions.

Zbl

DOI : 10.1051/ita:2006036

Classification : 68Q45
Mots-clés : descriptional complexity, finite-state automata, regular expressions

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     author = {Geffert, Viliam and I\v{s}to\v{n}ov\'a, L'ubom{\'\i}ra},
     title = {Conversion of regular expressions into realtime automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {611--629},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {4},
     year = {2006},
     doi = {10.1051/ita:2006036},
     zbl = {1110.68063},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2006036/}
}

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Geffert, Viliam; Ištoňová, L'ubomíra. Conversion of regular expressions into realtime automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 4, pp. 611-629. doi : 10.1051/ita:2006036. http://archive.numdam.org/articles/10.1051/ita:2006036/

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