Residual Nominal Automata

Authors Joshua Moerman , Matteo Sammartino

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Joshua Moerman
  • RTWH Aachen University, Germany
Matteo Sammartino
  • Royal Holloway University of London, UK
  • University College London, UK


We would like to thank Gerco van Heerdt for providing examples similar to that of ℒ_r in the context of probabilistic automata. We thank Borja Balle for references on residual probabilistic languages, and Henning Urbat for discussions on nominal lattice theory. Lastly, we thank the reviewers of a previous version of this paper for their interesting questions and suggestions.

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Joshua Moerman and Matteo Sammartino. Residual Nominal Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 44:1-44:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We are motivated by the following question: which nominal languages admit an active learning algorithm? This question was left open in previous work, and is particularly challenging for languages recognised by nondeterministic automata. To answer it, we develop the theory of residual nominal automata, a subclass of nondeterministic nominal automata. We prove that this class has canonical representatives, which can always be constructed via a finite number of observations. This property enables active learning algorithms, and makes up for the fact that residuality - a semantic property - is undecidable for nominal automata. Our construction for canonical residual automata is based on a machine-independent characterisation of residual languages, for which we develop new results in nominal lattice theory. Studying residuality in the context of nominal languages is a step towards a better understanding of learnability of automata with some sort of nondeterminism.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Automated reasoning
  • nominal automata
  • residual automata
  • derivative language
  • decidability
  • closure
  • exact learning
  • lattice theory


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