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Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl)

Author Quentin Aristote

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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • active learning
  • well quasi-orders
  • Valk-Jantzen lemma
  • piecewise-testable languages
  • monoids

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Abstract

We give a new proof of a result from well quasi-order theory on the computability of bases for upwards-closed sets of words. This new proof is based on Angluin’s L* algorithm, that learns an automaton from a minimally adequate teacher. This relates in particular two results from the 1980s: Angluin’s L* algorithm, and a result from Valk and Jantzen on the computability of bases for upwards-closed sets of tuples of integers.
Along the way, we describe an algorithm for learning quasi-ordered automata from a minimally adequate teacher, and extend a generalization of Valk and Jantzen’s result, encompassing both words and integers, to finitely generated monoids.

Cite As Get BibTex

Quentin Aristote. Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CALCO.2025.16

Author Details

Quentin Aristote
  • Université Paris Cité, CNRS, Inria, IRIF, F-75013, Paris, France

Funding

This work has received financial support from the European Research Council (ERC) under the European Union’s Horizon research and innovation program (grant agreement 101167526).

Acknowledgements

The author thanks Daniela Petrişan and anonymous reviewers for their precious comments.

References

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