Compact non-left-recursive grammars using the selective left-corner transform and factoring

TL;DR

This paper introduces a selective left-corner transform and factoring techniques to produce compact, non-left-recursive grammars that facilitate top-down parsing without significant size increase.

Contribution

It presents a novel selective left-corner transform combined with factorizations to generate smaller, non-left-recursive grammars from original ones.

Findings

Produces grammars not much larger than original

Enables top-down parsing for a subset of productions

Reduces size increase compared to standard transform

Abstract

The left-corner transform removes left-recursion from (probabilistic) context-free grammars and unification grammars, permitting simple top-down parsing techniques to be used. Unfortunately the grammars produced by the standard left-corner transform are usually much larger than the original. The selective left-corner transform described in this paper produces a transformed grammar which simulates left-corner recognition of a user-specified set of the original productions, and top-down recognition of the others. Combined with two factorizations, it produces non-left-recursive grammars that are not much larger than the original.