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arXiv · 2403.19526

Logic and Languages of Higher-Dimensional Automata

Amazigh Amrane·Hugo Bazille·Uli Fahrenberg·Marie Fortin
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Abstract

In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (iiPoms<=k) closed under order extension. We prove that languages of HDAs are MSO-definable. For the converse, we show that the order extensions of MSO-definable sets of iiPoms<=k are languages of HDAs. As a consequence, unlike the case of all pomsets, order extension of MSO-definable sets of iiPoms<=k is also MSO-definable.

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Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, Marie Fortin. 2024-03-28. Logic and Languages of Higher-Dimensional Automata. https://arxiv.org/abs/2403.19526

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