A New Constructive Method for the One-Letter Context-Free Grammars

Abstract

Constructive methods for obtaining the regular grammar counterparts for some sub-classes of the context free grammars (cfg) have been investigated by many researchers. An important class of grammars for which this is always possible is the one-letter cfg. We show in this paper a new constructive method for transforming arbitrary one-letter cfg to an equivalent regular expression of star-height 0 or 1. Our new result is considerably simpler than a previous construction by Leiss, and we also propose a new normal form for a regular expression with single-star occurrence. Through an alphabet factorization theorem, we show how to go beyond the one-letter cfg in a straight-forward way.