Fast Computations on Ordered Nominal Sets

  • David Venhoek
  • Joshua Moerman
  • Jurriaan Rot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11187)


We show how to compute efficiently with nominal sets over the total order symmetry, by developing a direct representation of such nominal sets and basic constructions thereon. In contrast to previous approaches, we work directly at the level of orbits, which allows for an accurate complexity analysis. The approach is implemented as the library Ons (Ordered Nominal Sets).

Our main motivation is nominal automata, which are models for recognising languages over infinite alphabets. 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.



We would like to thank Szymon Toruńczyk and Eryk Kopczyński for their prompt help when using the Lois library. For general comments and suggestions we would like to thank Ugo Montanari and Niels van der Weide. At last, we want to thank the anonymous reviewers for their comments.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute for Computing and Information SciencesRadboud UniversiteitNijmegenThe Netherlands

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