Residuality and Learning for Nondeterministic Nominal Automata

Joshua Moerman*, Matteo Sammartino*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We are motivated by the following question: which data languages admit an active learning algorithm? This question was left open in previous work by the authors, 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.
Original languageEnglish
Article number29
Number of pages28
JournalLogical Methods in Computer Science
Issue number1
Publication statusPublished - 3 Feb 2022


  • Closure
  • Decidability
  • Derivative language
  • Exact learning
  • Lattice theory
  • Nominal automata
  • Residual automata


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