A Tree Sampler for Bounded Context-Free Languages

TL;DR

This paper introduces a simple method for sampling trees from bounded context-free languages using an algebraic datatype to represent candidate parse forests, enabling efficient sampling and decoding.

Contribution

It presents a novel algebraic datatype for compactly representing parse forests in BCFLs and a straightforward sampling method from these representations.

Findings

Efficient sampling of trees from BCFLs achieved.

Compact representation of parse forests simplifies sampling process.

Method applicable to bounded context-free languages with or without replacement.

Abstract

In the following paper, we present a simple method for sampling trees with or without replacement from BCFLs. A BCFL is a context-free language (CFL) corresponding to an incomplete string with holes, which can be completed by valid terminals. To solve this problem, we introduce an algebraic datatype that compactly represents candidate parse forests for porous strings. Once constructed, sampling trees is a straightforward matter of sampling integers uniformly without replacement, then lazily decoding them into trees.