Fast computations on ordered nominal sets

David Venhoek, Joshua Moerman*, Jurriaan Rot

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Nominal automata are models for recognising languages over infinite alphabets, based on the algebraic notion of nominal set. Motivated by their use in automata theory, we show how to compute efficiently with nominal sets over the so-called total order symmetry, a variant which allows to compare alphabet letters for equality as well as their respective order. We develop an explicit finite representation of such nominal sets and basic constructions thereon. The approach is implemented as the library Ons (Ordered Nominal Sets), enabling programming with infinite sets. Returning to our motivation of nominal automata, we evaluate Ons in two applications: minimisation of automata and active automata learning. In both cases, Ons is competitive compared to existing implementations and outperforms them for certain classes of inputs.
Original languageEnglish
Pages (from-to)82-104
Number of pages23
JournalTheor. Comput. Sci.
Publication statusPublished - 31 Oct 2022


  • Automata learning
  • Automata theory
  • Minimisation
  • Nominal sets


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  • Fast Computations on Ordered Nominal Sets

    Venhoek, D., Moerman, J. & Rot, J., 16 Aug 2022, Cornell University - arXiv, 38 p. (Computing Research Repository).

    Research output: Working paper / PreprintPreprintAcademic

    Open Access
  • Fast Computations on Ordered Nominal Sets

    Venhoek, D., Moerman, J. & Rot, J., 2018, Theoretical Aspects of Computing- ICTAC 2018: 15th International Colloquium. Fischer, B. & Uustalu, T. (eds.). Springer, p. 493-512 20 p. (Lecture Notes in Computer Science, Vol. 11187). (Theoretical Computer Science and General Issues (LNCS subseries), Vol. 11187).

    Research output: Chapter in Book/Report/Conference proceedingConference Article in proceedingAcademicpeer-review

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