Logic and Languages of Higher-Dimensional Automata
Pages 51 - 67
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 () 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 are languages of HDAs. Furthermore, both constructions are effective. As a consequence, unlike the case of all pomsets, the order extension of any MSO-definable set of is MSO-definable.
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Aug 2024
310 pages
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
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Published: 12 August 2024
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