A new algorithm for regularizing one-letter context-free grammars

Authors:
Stefan Andrei;Salvador Valerio Cavadini;Wei-Ngan Chin
Affiliations:
CS Programme, Singapore-MIT Alliance, National University of Singapore, Singapore and Faculty of Computer Science, "Al.I. Cuza" University, Iasi, Romania;Centro de Inivestigación y Desarrollo de Software, Facultad de Matemática Aplicada, Universidad Católica de Santiago del Estero, Argentina;School of Computing, National University of Singapore, Singapore
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Constructive methods for obtaining regular grammar counterparts for some sub-classes of context-free grammars (CFGs) 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 an 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 only a single-star occurrence. Through an alphabet factorization theorem, we show how to go beyond the one-letter CFG in a straight-forward way.