On the Turing complexity of learning finite families of algebraic structures

Nikolay Bazhenov; Luca San Mauro

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arXiv · 2106.14515

On the Turing complexity of learning finite families of algebraic structures

Nikolay Bazhenov·Luca San Mauro

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Abstract

In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power that is needed to learn finite families of structures. In particular, we prove that, if a family of structures is both finite and learnable, then any oracle which computes the Halting set is able to achieve such a learning. On the other hand, we construct a pair of structures which is learnable but no computable learner can learn it.

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BibTeX RIS

Nikolay Bazhenov, Luca San Mauro. 2021-06-28. On the Turing complexity of learning finite families of algebraic structures. https://arxiv.org/abs/2106.14515

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