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Matrix Equations and Normal Forms for Context-Free Grammars

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Fundamental Problems in Computing

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Abstract

The relationship between the set of productions of a context-free grammar and the corresponding set of defining equations is first pointed out. The closure operation on a matrix of strings is defined and this concept is used to formalize the solution to a set of linear equations. A procedure is then given for rewriting a context-free grammar in Greibach normal form, where the replacement string of each production begins with a terminal symbol. An additional procedure is given for rewriting the grammar so that each replacement string both begins and ends with a terminal symbol. Neither procedure requires the evaluation of regular expressions over the total vocabulary of the grammar, as is required by Greibach’s procedure.

This work was written while the author was a National Science Foundation Graduate Fellow.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Columbia University, New York, NY, USA

    Daniel J. Rosenkrantz

Authors
  1. Daniel J. Rosenkrantz
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University at Albany—SUNY, 1400 Washington Avenue, Albany, NY, 12222, USA

    S. S. Ravi

  2. Bradley Dept. Electrical and Computer Engineering, Virginia Tech, 302 Whittemore (0111), Blacksburg, VA, 24061, USA

    Sandeep K. Shukla

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© 2009 Springer Science + Business Media B.V.

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Rosenkrantz, D.J. (2009). Matrix Equations and Normal Forms for Context-Free Grammars. In: Ravi, S.S., Shukla, S.K. (eds) Fundamental Problems in Computing. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9688-4_1

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  • DOI: https://doi.org/10.1007/978-1-4020-9688-4_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9687-7

  • Online ISBN: 978-1-4020-9688-4

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