# Nominal Topology for Data Languages

arXiv: https://arxiv.org/abs/2304.13337 · HTML: https://mlsanity.com/paper/2304.13337/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 52 references that are in the map.
- First posted on arXiv 26 Apr 2023.

## Builds on (most cited first, 8 of 8)

- [Automata theory in nominal sets](https://mlsanity.com/paper/1402.0897/) (2014)
- [A Robust Class of Data Languages and an Application to Learning](https://mlsanity.com/paper/1411.6646/) (2014)
- [Equational Axiomatization of Algebras with Structure](https://mlsanity.com/paper/1812.02016/) (2018)
- [Logics with rigidly guarded data tests](https://mlsanity.com/paper/1410.2022/) (2014)
- [Recognisable languages over monads](https://mlsanity.com/paper/1502.04898/) (2015)
- [Nominal Automata with Name Binding](https://mlsanity.com/paper/1603.01455/) (2016)
- [The Sch"utzenberger product for syntactic spaces](https://mlsanity.com/paper/1603.08264/) (2016)
- [Quantifiers on languages and codensity monads](https://mlsanity.com/paper/1702.08841/) (2017)

## Built on by (most cited first, 1 of 1)

- [The single-use restriction for register automata and transducers over infinite alphabets](https://mlsanity.com/paper/2406.18934/) (2024)

## Abstract (arXiv)

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.