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Translating regular expressions into small ε-free nondeterministic finite automata

  • Automata Theory I
  • Conference paper
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STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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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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References

  1. Ronald Book, Shimon Even, Sheila Greibach, and Gene Ott. Ambiguity in graphs and expressions. IEEE Trans. Comput, C-20(2):149–153, 1971.

    Google Scholar 

  2. Anne Brüggemann-Klein. Regular expressions into finite automata. Theoret. Comput. Sci., 120:197–213, 1993.

    Article  Google Scholar 

  3. Andrzej Ehrenfeucht and Paul Zeiger. Complexity measures for regular expressions. J. Comput. System Sci., 12:134–146, 1976.

    Google Scholar 

  4. V. M. Glushkov. The abstract theory of automata. Russian Math. Surveys, 16:1–53, 1961. Translation from Usp. Mat. Naut. 16:3–41, 1961 by J. M. Jackson.

    Article  Google Scholar 

  5. John E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, Mass., 1979.

    Google Scholar 

  6. Robert F. McNaughton and H. Yamada. Regular expressions and state graphs for automata. IRE Trans. Electron. Comput., EC-9(1):39–47, 1960.

    Google Scholar 

  7. Michael O. Rabin and Dana Scott. Finite automata and their decision problems. IBM J. Res. Develop., 3:114–125, 1959.

    Google Scholar 

  8. Seppo Sippu and Eljas Soisalon-Soininen. Parsing Theory, Vol. I: Languages and Parsing, volume 15 of EATCS Monographs on Theoret. Comput. Sci. Springer-Verlag, Berlin, 1988.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität zu Kiel, 24098, Kiel, Germany

    Juraj Hromkovič, Sebastian Seibert & Thomas Wilke

Authors
  1. Juraj Hromkovič
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  2. Sebastian Seibert
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  3. Thomas Wilke
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Rüdiger Reischuk Michel Morvan

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

  • eBook Packages: Springer Book Archive

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