Showing papers on "Formal grammar published in 1972"

Approximation of weighted type 0 languages by formal power series

Abstract: Productions of formal grammars may be given coefficients from certain semirings. These coefficients induce weights for both derivations in the grammar and strings over the terminal alphabet. The weighted grammars can be characterized by sets of equations, which in turn can be used to iteratively generate polynomial approximations to the weighted language. In order to study the sequence of approximations, we introduce the notion of a derivation in top-down form as a formalization of the concept of a derivation which rewrites all antecedents contained in a sentential form simultaneously. The height of a derivation in top-down form is the number of times the sentential form is rewritten. Our main result consists in establishing the relationship between the sequence of approximations of a weighted language and the derivations of a given height. This result is established for grammars in what we call standard form , but is not restricted to those grammars. As a corollary to our work, we show that every recursively enumerable set in V * can be expressed as an intersection of V * with the homomorphic image of a context-free language.