A survey of normal form covers for context-free grammars

An overview is given of cover results for normal forms of context-free grammars. The emphasis in this paper is on the possibility of constructing ɛ-free grammars, non-left-recursive grammars and grammars in Greibach normal form. Among others it is proved that any ɛ-free context-free grammar can be right covered with a context-free grammar in Greibach normal form. All the cover results concerning the ɛ-free grammars, the non-left-recursive grammars and the grammars in Greibach normal form are listed, with respect to several types of covers, in a cover-table

From left-regular to Greibach normal form grammars

Each context-free grammar can be transformed to a context-free grammar in Greibach normal form, that is, a context-free grammar where each right-hand side of a prorfuction begins with a terminal symbol and the remainder of the right-hand side consists of nonterminal symbols. In this short paper we show that for a left-regular grammar G we can obtain a right-regular grammar G’ (which is by definition in Greibach normal form) which left-to-right covers G (in this case left parses of G’ can be mapped by a homomorphism on right parses of G. Moreover, it is possible to obtain a context-free grammar G” in Greibach normal form which right covers the left-regular grammar G (in this case right parses of G” are mapped on right parses of G)