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Conversion of regular expressionsinto realtime automata

Published online by Cambridge University Press:  08 November 2006

Viliam Geffert  and
L'ubomíra Ištoňová
Viliam Geffert
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04001 Košice, Slovakia; [email protected]; [email protected]
L'ubomíra Ištoňová
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04001 Košice, Slovakia; [email protected]; [email protected]
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Abstract

We consider conversions of regular expressions into k-realtimefinite state automata, i.e., automata in which the number ofconsecutive 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 readingan input symbol, more than two times in a row, we show that theconversion of a regular expression into such an automaton producesonly O(n) states, O(nlogn) ε-transitions, and O(n)alphabet-transitions. We also show how to easily transform these2-realtime machines into 1-realtime automata, still with onlyO(nlogn) edges. These results contrast with the known lowerbound Ω(n(logn)2 / loglogn), holding for 0-realtimeautomata, i.e., for automata with no ε-transitions.

Keywords

Descriptional complexityfinite-state automataregularexpressions.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 4 , October 2006 , pp. 611 - 629
Copyright
© EDP Sciences, 2006

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