Active Learning of Upward-Closed Sets of Words
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913963432738816 |
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| author | Aristote, Quentin |
| author_facet | Aristote, Quentin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Active Learning of Upward-Closed Sets of Words Aristote, Quentin Formal Languages and Automata Theory F.4.3 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. |
| title | Active Learning of Upward-Closed Sets of Words |
| topic | Formal Languages and Automata Theory F.4.3 |
| url | https://arxiv.org/abs/2504.21429 |