Issue |
RAIRO-Theor. Inf. Appl.
Volume 40, Number 4, October-December 2006
|
|
---|---|---|
Page(s) | 611 - 629 | |
DOI | https://doi.org/10.1051/ita:2006036 | |
Published online | 08 November 2006 |
Conversion of regular expressions into realtime automata
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04001 Košice, Slovakia;
geffert@upjs.sk; lubomira.istonova@upjs.sk
Received:
25
April
2005
Accepted:
9
March
2006
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.
Mathematics Subject Classification: 68Q45
Key words: Descriptional complexity / finite-state automata / regular expressions.
© EDP Sciences, 2006
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