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

  • Authors:
  • Holger Petersen

  • Affiliations:
  • -

  • Venue:
  • STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
  • Year:
  • 2002

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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.