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Size, index, and context-sensitivity of controlled partition grammars

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Abstract

Controlled partition grammars (CPGs) were designed to apply to certain needs of linguists. General CPGs generate exactly all context-sensitive languages. CPGs have two parameters:size andindex. The partition index of CPGs can be bounded by two, while CPGs with partition index one generate exactly the class of context-free languages. The size (of the partition blocks) of CPGs can be bounded by two, while CPGs of size one generate a class of languages properly contained in the class of contextsensitive languages. If one can eliminate recursive productions of the formA→B in a CPG then deterministic and nondeterministic lba's are equivalent.

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Authors and Affiliations

  1. IBM T. J. Watson Research Center, P. O. Box 218, 10598, Yorktown Hgts., N.Y., USA

    Eva-Maria Mückstein Wotschke

  2. The Pennsylvania State University, 16802, University Park, Pennsylvania, USA

    Peter J. Downey

Authors
  1. Eva-Maria Mückstein Wotschke
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  2. Detlef Wotschke
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  3. Peter J. Downey
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Additional information

This author was supported in part by NSF Grant No. MCS 76-10076.

This author was supported in part by NSF Grant No. MCS 75-22557.

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Mückstein Wotschke, EM., Wotschke, D. & Downey, P.J. Size, index, and context-sensitivity of controlled partition grammars. Math. Systems Theory 11, 47–60 (1977). https://doi.org/10.1007/BF01768467

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  • DOI: https://doi.org/10.1007/BF01768467

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