Formal languages and power series
Donald F. Stanat · 1971
Section 1 of this paper presents the basic mathematical definitions for our work. Section 2 defines the notion of a weighted phrase-structure grammar over either a semiring or zero monoid coefficient structure. The notion of canonical derivations (from Griffiths [1968]) and top-down derivations is defined in section 3, along with some of their basic properties. Equivalence relations over weighted phrase-structure grammars are defined in section 4 as well as power series representations of the associated languages.