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Calculating the Mind Change Complexity of Learning Algebraic Structures

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Revolutions and Revelations in Computability (CiE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13359))

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Abstract

This paper studies algorithmic learning theory applied to algebraic structures. In previous papers, we have defined our framework, where a learner, given a family of structures, receives larger and larger pieces of an arbitrary copy of a structure in the family and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if there is a learner that eventually stabilizes to a correct conjecture. Here, we analyze the number of mind changes that are needed to learn a given family \(\mathfrak {K}\). We give a descriptive set-theoretic interpretation of such mind change complexity. We also study how bounding the Turing degree of learners affects the mind change complexity of a given family of algebraic structures.

Bazhenov was supported by the Ministry of Education and Science of the Republic of Kazakhstan, grant AP08856493 “Positive graphs and computable reducibility on them as mathematical model of databases”. Cipriani’s research was partially supported by the Italian PRIN 2017 Grant “Mathematical Logic: models, sets, computability”. We also thank the anonymous referees for their careful reading of the paper and the valuable suggestions.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Nikolay Bazhenov

  2. Università degli Studi di Udine, Udine, Italy

    Vittorio Cipriani

  3. Sapienza Università di Roma, Roma, Italy

    Luca San Mauro

Authors
  1. Nikolay Bazhenov
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  2. Vittorio Cipriani
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  3. Luca San Mauro
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Corresponding author

Correspondence to Vittorio Cipriani .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, UK

    Ulrich Berger

  2. Department of Mathematics, Hofstra University, Hempstead, NY, USA

    Johanna N. Y. Franklin

  3. Georg-August University Göttingen, Göttingen, Germany

    Florin Manea

  4. Department of Computer Science, Swansea University, Swansea, UK

    Arno Pauly

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Bazhenov, N., Cipriani, V., San Mauro, L. (2022). Calculating the Mind Change Complexity of Learning Algebraic Structures. In: Berger, U., Franklin, J.N.Y., Manea, F., Pauly, A. (eds) Revolutions and Revelations in Computability. CiE 2022. Lecture Notes in Computer Science, vol 13359. Springer, Cham. https://doi.org/10.1007/978-3-031-08740-0_1

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  • DOI: https://doi.org/10.1007/978-3-031-08740-0_1

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