Structural equivalance and LL-k grammers

It has been shown by Lewis and Stearns that LL-k grammars are useful descriptive forms for languages that are to be translated mechanically. The goal of the research reported on here is to develop algorithms for transforming arbitrary context-free grammars into LL-k grammars while retaining the structure imposed on the language by the grammar, if this is possible. A solution is presented for the case where k=1 and there are no ∈-rules. In addition it is shown that every LL-k grammar is structurally equivalent to what we define as an LL*-k grammar, a form with a simpler definition that leads to a simpler parsing algorithm. It is hoped that this latter result will facilitate the generalization of the former result.