On the Turing complexity of learning finite families of algebraic structures
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 structu...
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| Veröffentlicht in: | Journal of logic and computation 2021-10, Vol.31 (7), p.1891-1900 |
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| container_end_page | 1900 |
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| container_issue | 7 |
| container_start_page | 1891 |
| container_title | Journal of logic and computation |
| container_volume | 31 |
| creator | Bazhenov, Nikolay San Mauro, Luca |
| description | 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. |
| doi_str_mv | 10.1093/logcom/exab044 |
| format | Article |
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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.</description><issn>0955-792X</issn><issn>1465-363X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNqFkDlrwzAYhkVpoW7atbPWDk50-hhL6AWGLClkM7LyyVWRDyQZkn_fGGfv9MJ7DQ9Cz5SsKSn5xg2tHroNnFRDhLhBCRWZTHnGD7coIaWUaV6ywz16COGXEMIyKhJU7XocfwDvJ2_7Fl8ORgcnG894MNiB8v1sG9vbCNiozjoLYc6Ua6Hxymocop90nDyER3RnlAvwdNUV-n5_228_02r38bV9rVLNch7TIwjKS1CyyDjkpjFgONcFFwCs0AVjRyOhpMLQJmeCcCoZk7RQjEImCWV8hdbLr_ZDCB5MPXrbKX-uKalnFvXCor6yuAxelsEwjf91_wC9pGPK</recordid><startdate>20211001</startdate><enddate>20211001</enddate><creator>Bazhenov, Nikolay</creator><creator>San Mauro, Luca</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20211001</creationdate><title>On the Turing complexity of learning finite families of algebraic structures</title><author>Bazhenov, Nikolay ; San Mauro, Luca</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c273t-de4139ea5863e7fbfef33c834ee28c822df5e914f1b724031522518a21e650123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bazhenov, Nikolay</creatorcontrib><creatorcontrib>San Mauro, Luca</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of logic and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bazhenov, Nikolay</au><au>San Mauro, Luca</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Turing complexity of learning finite families of algebraic structures</atitle><jtitle>Journal of logic and computation</jtitle><date>2021-10-01</date><risdate>2021</risdate><volume>31</volume><issue>7</issue><spage>1891</spage><epage>1900</epage><pages>1891-1900</pages><issn>0955-792X</issn><eissn>1465-363X</eissn><abstract>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.</abstract><pub>Oxford University Press</pub><doi>10.1093/logcom/exab044</doi><tpages>10</tpages></addata></record> |
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| ispartof | Journal of logic and computation, 2021-10, Vol.31 (7), p.1891-1900 |
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| language | eng |
| recordid | cdi_crossref_primary_10_1093_logcom_exab044 |
| source | Oxford University Press Journals All Titles (1996-Current) |
| title | On the Turing complexity of learning finite families of algebraic structures |
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