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The Membership Problem for Regular Expressions with Intersection Is Complete in LOGCFL

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

We show that the recognition problem of context-free languages can be reduced to membership in the language defined by a regular expression with intersection by a log space reduction with linear output length. We also show a matching upper bound improving the known fact that the membership problem for these regular expressions is in NC2. Together these results establish that the membership problem is complete in LOGCFL. For unary expressions we show hardness for the class NL and some related results.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Stuttgart, Breitwiesenstr. 20-22, D-70565, Stuttgart

    Holger Petersen

Authors
  1. Holger Petersen
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Petersen, H. (2002). The Membership Problem for Regular Expressions with Intersection Is Complete in LOGCFL. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_42

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  • DOI: https://doi.org/10.1007/3-540-45841-7_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

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