Conversion of regular expressions into realtime automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 4, pp. 611-629.

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(nlogn) 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(nlogn) edges. These results contrast with the known lower bound Ω(n(logn) 2 /loglogn), holding for 0-realtime automata, i.e., for automata with no ε-transitions.

DOI: 10.1051/ita:2006036
Classification: 68Q45
Keywords: descriptional complexity, finite-state automata, regular expressions
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     title = {Conversion of regular expressions into realtime automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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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, Volume 40 (2006) no. 4, pp. 611-629. doi : 10.1051/ita:2006036. http://www.numdam.org/articles/10.1051/ita:2006036/

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