A Unifying Approach to Picture Automata

2025-09-15

AI Summary

This paper addresses the problem of two-dimensional image-language recognition. It proposes a unified modeling framework based on directed acyclic graph (DAG) automata. By encoding two-dimensional strings or images as DAG structures, the framework systematically compares input-agnostic versus input-driven encoding strategies: the former subsumes classical models—including regression finite automata, turning automata, and online tiling automata—while the latter substantially enhances recognition capacity, enabling DAG automata to accept certain context-sensitive languages for the first time and thus surpassing the expressive limits of online tiling automata. The key contribution is the introduction of an input-driven encoding mechanism, which extends the recognized language class from standard two-dimensional regular languages to strictly more powerful ones. Within this unified framework, the paper rigorously characterizes the language-acceptance capabilities of multiple classes of image automata.

Technology Category

• Computer Vision: Language and Vision
• Machine Learning: Structured Learning
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

A directed acyclic graph (DAG) can represent a two-dimensional string or picture. We propose recognizing picture languages using DAG automata by encoding 2D inputs into DAGs. An encoding can be input-agnostic (based on input size only) or input-driven (depending on symbols). Three distinct input-agnostic encodings characterize classes of picture languages accepted by returning finite automata, boustrophedon automata, and online tessellation automata. Encoding a string as a simple directed path limits recognition to regular languages. However, input-driven encodings allow DAG automata to recognize some context-sensitive string languages and outperform online tessellation automata in two dimensions.

Problem

• Propose recognizing picture languages using DAG automata
• Characterize classes accepted by different automata types
• Enable recognition beyond regular languages with input-driven encodings

Innovation

• DAG automata for picture recognition
• Input-agnostic and input-driven encodings
• Recognizes context-sensitive string languages