English

A Unifying Approach to Picture Automata

Formal Languages and Automata Theory 2026-05-26 v1

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.

Keywords

Cite

@article{arxiv.2509.12077,
  title  = {A Unifying Approach to Picture Automata},
  author = {Yvo Ad Meeres and František Mráz},
  journal= {arXiv preprint arXiv:2509.12077},
  year   = {2026}
}

Comments

A full version of a paper for ITAT WAFNL 2025