# Generic Axiomatization of Families of Noncrossing Graphs in Dependency Parsing

## TL;DR

This paper introduces a unified encoding for noncrossing graphs in dependency parsing, enabling a single inference algorithm to handle multiple graph families by controlling search space through forbidden patterns.

## Contribution

It provides a simple latent encoding that represents various noncrossing graph families as context-free languages, simplifying inference in dependency parsing.

## Key findings

- Encoding captures multiple graph families as context-free languages
- Unified inference algorithm applicable to all families
- Elimination of family-specific differentiation in parsing algorithms

## Abstract

We present a simple encoding for unlabeled noncrossing graphs and show how its latent counterpart helps us to represent several families of directed and undirected graphs used in syntactic and semantic parsing of natural language as context-free languages. The families are separated purely on the basis of forbidden patterns in latent encoding, eliminating the need to differentiate the families of non-crossing graphs in inference algorithms: one algorithm works for all when the search space can be controlled in parser input.

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Source: https://tomesphere.com/paper/1706.03357