LR Parsing of Permutation Phrases

TL;DR

This paper introduces an efficient LR parsing algorithm for permutation phrases that significantly reduces the number of states needed, making parsing more practical for real-world applications like JSON.

Contribution

It presents a novel LR(0) automaton construction that drastically reduces state complexity for permutation phrase parsing.

Findings

State count reduced from Ω(n!) to O(2^n)

More compact parsing tables for longer permutation phrases

Effective application demonstrated on JSON parsing

Abstract

This paper presents an efficient method for LR parsing of permutation phrases. In practical cases, the proposed algorithm constructs an LR(0) automaton that requires significantly fewer states to process a permutation phrase compared to the standard construction. For most real-world grammars, the number of states is typically reduced from $\Omega(n!)$ to $O(2^{n})$, resulting in a much more compact parsing table. The state reduction increases with longer permutation phrases and a higher number of permutation phrases within the right-hand side of a rule. We demonstrate the effectiveness of this method through its application to parsing a JSON document.