On the Transformation of LL(k)-linear Grammars to LL(1)-linear

Abstract

It is proved that every LL(k)-linear grammar can be transformed to an equivalent LL(1)-linear grammar. The transformation incurs a blow-up in the number of nonterminal symbols by a factor of $$m^{2k-O(1)}$$, where m is the size of the alphabet. A close lower bound is established: for certain LL(k)-linear grammars with n nonterminal symbols, every equivalent LL(1)-linear grammar must have at least $$n \cdot (m-1)^{2k-O(\log k)}$$ nonterminal symbols.