# The Weighted CFG Constraint

## TL;DR

This paper introduces the weighted CFG constraint and presents an efficient propagation algorithm that enforces domain consistency, which can be decomposed into primitive constraints without losing effectiveness.

## Contribution

The paper proposes a novel weighted CFG constraint and an associated propagation algorithm with cubic time complexity, enabling efficient constraint solving.

## Key findings

- Propagation algorithm enforces domain consistency in O(n^3|G|) time.
- Decomposition into primitive constraints does not hinder propagation.
- The approach enhances constraint programming with weighted context-free grammars.

## Abstract

We introduce the weighted CFG constraint and propose a propagation algorithm that enforces domain consistency in $O(n^3|G|)$ time. We show that this algorithm can be decomposed into a set of primitive arithmetic constraints without hindering propagation.