Control sets on grammars

Given a setC of strings of rewriting rules of a phrase structure grammarG, we consider the setLc(G) of those words generated by leftmost derivations inG whose corresponding string of rewriting rules is an element ofC. The paper concerns the nature of the setLc(G) whenC andG are assumed to have special form. For example, forG an arbitrary phrase structure grammar,Lc(G) is an abstract family of languages ifC is an abstract family of languages, andLc(G) is bounded ifC is bounded.