Eliminating Left Recursion without the Epsilon

TL;DR

This paper presents a revised algorithm for eliminating left recursion in grammars that avoids exponential blow-up and preserves parse tree detail, making it practical for real-world use.

Contribution

The authors introduce a graph-theoretic approach to eliminate indirect left recursion and extend the algorithm to recover original parse trees, improving upon standard methods.

Findings

The revised algorithm effectively eliminates left recursion without exponential complexity.

It preserves parse tree detail that standard algorithms often lose.

The method is practical and applicable to real-world grammar processing.

Abstract

The standard algorithm to eliminate indirect left recursion takes a preventative approach, rewriting a grammar's rules so that indirect left recursion is no longer possible, rather than eliminating it only as and when it occurs. This approach results in many of the rules being lost, so that the parse trees that result are often devoid of the detail that the BNF was supposed to capture in the first place. Furthermore, the standard algorithm results in exponential blow-up as the BNF is rewritten, making it wholly unworkable in practice. To avoid these pitfalls, we revise the standard algorithm to eliminate direct left recursion and then take a graph-theoretic approach to eliminating indirect left recursion. We also extend the algorithm to rewrite the resultant parse trees in order to recover the parse trees that would have resulted if left recursion had not had to be eliminated in the first place. Therefore, aside from a couple of caveats, our algorithm works not just in theory but also in practice.