Detalles Bibliográficos
| Title: |
B\'uchi-Elgot-Trakhtenbrot Theorem for Higher-Dimensional Automata |
| Autores: |
Amrane, Amazigh, Bazille, Hugo, Clement, Emily, Fahrenberg, Uli, Fortin, Marie, Ziemiański, Krzysztof |
| Ano de Publicación: |
2025 |
| Colección: |
Computer Science |
| Subject Terms: |
Computer Science - Formal Languages and Automata Theory |
| Descripción: |
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. |
| Tipo de documento: |
Working Paper |
| URL de acceso: |
http://arxiv.org/abs/2505.10461 |
| Número de acceso: |
edsarx.2505.10461 |
| Base de Datos: |
arXiv |