Reduction of Scattered Context Generators of Sentences Preceded by Their Leftmost Parses

This paper uses scattered context grammars to derive their sentences preceded by corresponding parses--the sequences of labels of productions used during the derivation. It discusses their canonical versions, which make this derivation in a leftmost way, and demonstrates that for every recursively enumerable language, L, there exists a scattered context generator whose language consists of L's sentences preceded by their leftmost parses. In fact, this demonstration is achieved based on generators with a reduced number of nonterminals.