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Substitution of grammar forms

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Summary

Given grammar forms F and F′, the grammar form Sûb (F, Ft') is defined as that obtained by substituting the start variable of F′ for every occurrence of a terminal in F. The main result is that if F is a nontrivial grammar form, then the grammatical family defined by Sûb (F, F′) is the set of languages obtained by substituting languages in the family defined by F′ into the family defined by F. Thus the substitution of one grammatical family into another is a grammatical family. It follows as a corollary that the full AFL generated by a grammatical family is a grammatical family.

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References

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Authors and Affiliations

  1. Computer Science Program, University of Southern California, 90007, University Park Los Angeles, Calif., USA

    Seymour Ginsburg

  2. Department of Mathematics, University of California at Berkeley, 94720, Berkeley, Calif., USA

    Edwin H. Spanier

Authors
  1. Seymour Ginsburg
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  2. Edwin H. Spanier
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Additional information

This research was supported in part by a Guggenheim fellowship and by NSF Grant No. 42306.

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Ginsburg, S., Spanier, E.H. Substitution of grammar forms. Acta Informatica 5, 377–386 (1975). https://doi.org/10.1007/BF00264567

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  • DOI: https://doi.org/10.1007/BF00264567

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