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 con text-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). More general results on covers for context-free gwnmars in Greiharh -WW~ form and in non-leftrecursive F . 2; UC: round in (6,8,13]. Negative cover results appear in [ 141. Complexity problems for covers for regular and linear grammars can be found in [S,S] . Covers, in the sense that we will use them here, were introduced by Gray and Harrison [2,3] and they are also considered in [ I] . However, as will be seen, our definition is slightly different from theirs, and this difference is essential to obtain the results in-this paper. Other papers in which types of covers are introduced are [ 10,111.