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arXiv · 2504.21429

Active Learning of Upward-Closed Sets of Words

Quentin Aristote
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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.

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Quentin Aristote. 2025-04-30. Active Learning of Upward-Closed Sets of Words. https://doi.org/10.4230/lipics.calco.2025.16

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