Abstract
It is proved that every regular expression of size n can be converted into an equivalent nondeterministic finite automaton (NFA) of size O(n(log n)2) in polynomial time. The best previous conversions result in NFAs of worst case size Θ(n 2). Moreover, the nonexistence of any linear conversion is proved: we give a language L n described by a regular expression of size O(n) such that every NFA accepting L n is of size Ω(n log n).
Supported by the Deutsche Forschungsgemeinschaft under project no. HR 14/3-1.
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© 1997 Springer-Verlag Berlin Heidelberg
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Hromkovič, J., Seibert, S., Wilke, T. (1997). Translating regular expressions into small ε-free nondeterministic finite automata. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023448
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DOI: https://doi.org/10.1007/BFb0023448
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