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It is proved that every regular expression of size n can be converted into an equivalent nondeterministic nite automaton (NFA) of size O(n(log n) 2) in polynomial time. The best previous conversions result in NFAs of worst case size (n 2). Moreover, the nonexistence of any linear conversion is proved: we give a language Ln described by a regular expression of size O(n) such that every NFA accepting Ln is of size (n log n).

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