Separation and Renaming in Nominal Sets

Authors Joshua Moerman, Jurriaan Rot

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Author Details

Joshua Moerman
  • RWTH Aachen University, Germany
Jurriaan Rot
  • University College London, United Kingdom and Radboud University, The Netherlands


We would like to thank Jamie Gabbay, Gerco van Heerdt, Tom Hirschowitz, Bart Jacobs, and the anonymous reviewers for their useful comments.

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Joshua Moerman and Jurriaan Rot. Separation and Renaming in Nominal Sets. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which involve arbitrary substitutions rather than permutations, through a categorical adjunction. In particular, the left adjoint relates the separated product of nominal sets to the Cartesian product of nominal renaming sets. Based on these results, we define the new notion of separated nominal automata. We show that these automata can be exponentially smaller than classical nominal automata, if the semantics is closed under substitutions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Nominal sets
  • Separated product
  • Adjunction
  • Automata
  • Coalgebra


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