On the Turing complexity of learning finite families of algebraic structures
Logic
2021-06-29 v1
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.
Keywords
Cite
@article{arxiv.2106.14515,
title = {On the Turing complexity of learning finite families of algebraic structures},
author = {Nikolay Bazhenov and Luca San Mauro},
journal= {arXiv preprint arXiv:2106.14515},
year = {2021}
}
Comments
11 pages, 1 figure, accepted for publication in the Journal of Logic and Computation