Prefix Parsing is Just Parsing

TL;DR

This paper introduces a novel, efficient method for prefix parsing by transforming grammars, enabling the use of standard parsing algorithms for prefix and weighted prefix parsing tasks.

Contribution

The authors present the prefix grammar transformation, allowing prefix parsing to be performed with ordinary parsers, and develop a strategy for efficiently computing prefix weights.

Findings

The transformed grammar is only a small factor larger than the original.

Any optimized parser can be used directly on the transformed grammar.

The framework enables efficient prediction of next tokens in language modeling.

Abstract

Prefix parsing asks whether an input prefix can be extended to a complete string generated by a given grammar. In the weighted setting, it also provides prefix probabilities, which are central to context-free language modeling, psycholinguistic analysis, and syntactically constrained generation from large language models. We introduce the prefix grammar transformation, an efficient reduction of prefix parsing to ordinary parsing. Given a grammar, our method constructs another grammar that generates exactly the prefixes of its original strings. Prefix parsing is then solved by applying any ordinary parsing algorithm on the transformed grammar without modification. The reduction is both elegant and practical: the transformed grammar is only a small factor larger than the input, and any optimized implementation can be used directly, eliminating the need for bespoke prefix-parsing algorithms. We also present a strategy-based on algorithmic differentiation-for computing the next-token weight vector, i.e., the prefix weights of all one-token extensions, enabling efficient prediction of the next token. Together, these contributions yield a simple, general, and efficient framework for prefix parsing.