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arXiv · 2304.13337

Nominal Topology for Data Languages

Fabian Birkmann·Stefan Milius·Henning Urbat
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Abstract

We propose a novel topological perspective on data languages recognizable by orbit-finite nominal monoids. For this purpose, we introduce pro-orbit-finite nominal topological spaces. Assuming globally bounded support sizes, they coincide with nominal Stone spaces and are shown to be dually equivalent to a subcategory of nominal boolean algebras. Recognizable data languages are characterized as topologically clopen sets of pro-orbit-finite words. In addition, we explore the expressive power of pro-orbit-finite equations by establishing a nominal version of Reiterman's pseudovariety theorem.

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Fabian Birkmann, Stefan Milius, Henning Urbat. 2023-04-26. Nominal Topology for Data Languages. https://doi.org/10.4230/lipics.icalp.2023.114

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