On Learning for Families of Algebraic Structures
Nikolay A. Bazhenov · Lobachevskii Journal of Mathematics · 2024
We survey the recent results on algorithmic learning for families of countable algebraic structures. Within this framework, at each step a learner obtains a finite amount of data about a given countable structure $$S$$ (which is supposed to be learned), and then the learner outputs a conjecture describing the isomorphism type of $$S$$ . If the sequence of conjectures converges to the correct answer, then the learning procedure is successful. The paper discusses the results connecting learnability with syntactic properties of structures $$S$$ . We also give some results on the new approach to learnability which uses equivalence relations on the Cantor space.