B\"uchi-Elgot-Trakhtenbrot Theorem for Higher-Dimensional Automata
Formal Languages and Automata Theory
2025-05-16 v1
Abstract
In this paper we explore languages of higher-dimensional automata (HDAs) from an algebraic and logical point of view. Such languages are sets of finite width-bounded interval pomsets with interfaces (ipomsets) closed under order extension. We show that ipomsets can be represented as equivalence classes of words over a particular alphabet, called step sequences. We introduce an automaton model that recognize such languages. Doing so allows us to lift the classical B\"uchi-Elgot-Trakhtenbrot Theorem to languages of HDAs: we prove that a set of interval ipomsets is the language of an HDA if and only if it is simultaneously MSO-definable, of bounded width, and closed under order refinement.
Keywords
Cite
@article{arxiv.2505.10461,
title = {B\"uchi-Elgot-Trakhtenbrot Theorem for Higher-Dimensional Automata},
author = {Amazigh Amrane and Hugo Bazille and Emily Clement and Uli Fahrenberg and Marie Fortin and Krzysztof Ziemiański},
journal= {arXiv preprint arXiv:2505.10461},
year = {2025}
}