Ordered Context-Free Grammars Revisited

TL;DR

This paper revisits ordered context-free grammars, offering a simplified derivation definition and a parsing algorithm with O(n^4) complexity, enhancing understanding and computational efficiency of this formalism.

Contribution

It simplifies the derivation process and introduces a new parsing algorithm for ordered context-free grammars with improved complexity.

Findings

Simplified the derivation definition for ordered context-free grammars

Developed a parsing algorithm with O(n^4) time complexity

Enhanced the computational understanding of ordered context-free grammars

Abstract

We continue our study of ordered context-free grammars, a grammar formalism that places an order on the parse trees produced by the corresponding context-free grammar. In particular, we simplify our previous definition of a derivation of a string for a given ordered context-free grammar, and present a parsing algorithm, using shared packed parse forests, with time complexity O(n^4), where n is the length of the input string being parsed.