On Learning for Families of Algebraic Structures

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.