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On Learning for Families of Algebraic Structures. / Bazhenov, N. A.

In: Lobachevskii Journal of Mathematics, Vol. 45, No. 4, 04.2024, p. 1789-1799.

Research output: Contribution to journal › Article › peer-review

Harvard

Bazhenov, NA 2024, 'On Learning for Families of Algebraic Structures', Lobachevskii Journal of Mathematics, vol. 45, no. 4, pp. 1789-1799. https://doi.org/10.1134/S1995080224601334

APA

Bazhenov, N. A. (2024). On Learning for Families of Algebraic Structures. Lobachevskii Journal of Mathematics, 45(4), 1789-1799. https://doi.org/10.1134/S1995080224601334

Vancouver

Bazhenov NA. On Learning for Families of Algebraic Structures. Lobachevskii Journal of Mathematics. 2024 Apr;45(4):1789-1799. doi: 10.1134/S1995080224601334

Author

Bazhenov, N. A. / On Learning for Families of Algebraic Structures. In: Lobachevskii Journal of Mathematics. 2024 ; Vol. 45, No. 4. pp. 1789-1799.

BibTeX

@article{526d60b45036416d955ff553cbb0b5e2,
title = "On Learning for Families of Algebraic Structures",
abstract = "Abstract: 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 (which is supposed to be learned), and then the learner outputs a conjecture describing the isomorphism type of. 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. We also give some results on the new approach to learnability which uses equivalence relations on the Cantor space.",
keywords = "Borel equivalence relation, algorithmic learning theory, computable structure, inductive inference, infinitary formulas",
author = "Bazhenov, {N. A.}",
note = "The work is supported by the Mathematical Center in Akademgorodok under the agreement no. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.",
year = "2024",
month = apr,
doi = "10.1134/S1995080224601334",
language = "English",
volume = "45",
pages = "1789--1799",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "4",

}

RIS

TY - JOUR

T1 - On Learning for Families of Algebraic Structures

AU - Bazhenov, N. A.

N1 - The work is supported by the Mathematical Center in Akademgorodok under the agreement no. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/4

Y1 - 2024/4

N2 - Abstract: 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 (which is supposed to be learned), and then the learner outputs a conjecture describing the isomorphism type of. 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. We also give some results on the new approach to learnability which uses equivalence relations on the Cantor space.

AB - Abstract: 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 (which is supposed to be learned), and then the learner outputs a conjecture describing the isomorphism type of. 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. We also give some results on the new approach to learnability which uses equivalence relations on the Cantor space.

KW - Borel equivalence relation

KW - algorithmic learning theory

KW - computable structure

KW - inductive inference

KW - infinitary formulas

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85201791671&origin=inward&txGid=182b1cc6d9e3bd9381f9c2ce08d3cdd7

UR - https://www.mendeley.com/catalogue/8e1deb8c-e2d6-3e71-bf59-fdc2c9b9dc83/

U2 - 10.1134/S1995080224601334

DO - 10.1134/S1995080224601334

M3 - Article

VL - 45

SP - 1789

EP - 1799

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 4

ER -

ID: 61056991