A homomorphism theorem for weighted context-free grammars

  • Authors:

  • Donald F. Stanat

  • Affiliations:

  • -

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1972

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Abstract

Productions of a context-free grammar can be given coefficients from semirings, inducing weights for both derivations in the grammar and strings over the terminal alphabet. For a weighted context-free grammar in Greibach normal form, the weight of any string, as well as the set of derivations of the string, may be determined from the image under a homomorphism which maps each terminal symbol to a polynomial. The definition of the homomorphism is a straightforward function of the productions. Some examples of interesting semiring structures are included.