A Note on the Generative Power of Some Simple Variants of Context-Free Grammars Regulated by Context Conditions

This paper answers three open questions concerning the generative power of some simple variants of context-free grammars regulated by context conditions. Specifically, it discusses the generative power of so-called context-free semi-conditional grammars (which are random context grammars where permitting and forbidding sets are replaced with permitting and forbidding strings) where permitting and forbidding strings of each production are of length no more than one, and of simple semi-conditional grammars where, in addition, no production has attached both a permitting and a forbidding string. Finally, this paper also presents some normal form results, an overview of known results, and unsolved problems.