Supported Sets - A New Foundation for Nominal Sets and Automata

Author Thorsten Wißmann

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Thorsten Wißmann
  • Radboud University, Nijmegen, the Netherlands


The author thanks Jurriaan Rot, Joshua Moerman, and Frits Vaandrager for inspiring discussions. The definition of supported sets originated from discussions with Lutz Schröder, Dexter Kozen, and Stefan Milius.

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Thorsten Wißmann. Supported Sets - A New Foundation for Nominal Sets and Automata. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all these differently flavoured categories of nominal sets are monadic over supported sets. Thus, supported sets provide a canonical finite way to represent nominal sets and the automata therein, e.g. register automata and coalgebras in general. Name binding in supported sets is modelled by a functor following the idea of de Bruijn indices. This functor lifts to the well-known abstraction functor in nominal sets. Together with the monadicity result, this gives rise to a transformation process from finite coalgebras in supported sets to orbit-finite coalgebras in nominal sets. One instance of this process transforms the finite representation of a register automaton in supported sets into its configuration automaton in nominal sets.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Nominal Sets
  • Monads
  • LFP-Category
  • Supported Sets
  • Coalgebra


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