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Computing ε-free NFA from regular expressions in O(n log2(N)) time

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

The standard procedure to transform a regular expression to an ε-free NFA yields a quadratic blow-up of the number of transitions. For a long time this was viewed as an unavoidable fact. Recently Hromkovič et.al. [5] exhibited a construction yielding ε-free NFA with O(n log2(n)) transitions. A rough estimation of the time needed for their construction shows a cubic time bound. The known lower bound is Ω(n log(n)). In this paper we present a sequential algorithm for the construction described in [5] which works in time O(n log(n) + size of the output). On a CREW PRAM the construction is possible in time O(log(n)) using O(n + (size of the output)/log(n)) processors.

Research was partly supported by the French-German project PROCOPE.

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References

  1. G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117–126, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Brüggemann-Klein. Regular expressions into finite automata. Theoretical Computer Science, 120:197–213, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Ehrenfeucht and P. Zeiger. Complexity measures for regular expressions. Journal of Computer and System Sciences, 12:134–146, 1976.

    MATH  MathSciNet  Google Scholar 

  4. A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, 1989.

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  5. J. Hromkovič, S. Seibert, and T. Wilke. Translating regular expressions into small ε-free nondeterministic finite automata. In Proc. of the 14th Ann. Symp. on Theor. Aspects of Comp. Sci. (STACS'97), no. 1200 in LNCS, p. 55–66, 1997. Springer.

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Authors and Affiliations

  1. Institut für Informatik, Universität Stuttgart, Breitwiesenstr. 20-22, 70565, Stuttgart, Germany

    Christian Hagenah & Anca Muscholl

Authors
  1. Christian Hagenah
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  2. Anca Muscholl
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Hagenah, C., Muscholl, A. (1998). Computing ε-free NFA from regular expressions in O(n log2(N)) time. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055777

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  • DOI: https://doi.org/10.1007/BFb0055777

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

  • eBook Packages: Springer Book Archive

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