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A minimal substitution basis for the Kalmár elementary functions.

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Title: A minimal substitution basis for the Kalmár elementary functions.
Authors: Prunescu, Mihai1 (AUTHOR), Sauras-Altuzarra, Lorenzo2 (AUTHOR), Shunia, Joseph M3 (AUTHOR)
Source: Journal of Logic & Computation. Apr2026, Vol. 36 Issue 3, p1-10. 10p.
Subjects: Addition (Mathematics), Modular arithmetic, Binary operations, Computable functions
Abstract: We show that the class of Kalmár elementary functions can be inductively generated from the addition, the integer remainder and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. We also prove that the substitution basis defined by these three operations is minimal. Furthermore, we discuss alternative substitution bases under arity constraints. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193363970
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: A minimal substitution basis for the Kalmár elementary functions.
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  Data: <searchLink fieldCode="AR" term="%22Prunescu%2C+Mihai%22">Prunescu, Mihai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sauras-Altuzarra%2C+Lorenzo%22">Sauras-Altuzarra, Lorenzo</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Shunia%2C+Joseph+M%22">Shunia, Joseph M</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="DE" term="%22Addition+%28Mathematics%29%22">Addition (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Modular+arithmetic%22">Modular arithmetic</searchLink><br /><searchLink fieldCode="DE" term="%22Binary+operations%22">Binary operations</searchLink><br /><searchLink fieldCode="DE" term="%22Computable+functions%22">Computable functions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We show that the class of Kalmár elementary functions can be inductively generated from the addition, the integer remainder and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. We also prove that the substitution basis defined by these three operations is minimal. Furthermore, we discuss alternative substitution bases under arity constraints. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1093/logcom/exag010
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 10
        StartPage: 1
    Subjects:
      – SubjectFull: Addition (Mathematics)
        Type: general
      – SubjectFull: Modular arithmetic
        Type: general
      – SubjectFull: Binary operations
        Type: general
      – SubjectFull: Computable functions
        Type: general
    Titles:
      – TitleFull: A minimal substitution basis for the Kalmár elementary functions.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Prunescu, Mihai
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          Name:
            NameFull: Sauras-Altuzarra, Lorenzo
      – PersonEntity:
          Name:
            NameFull: Shunia, Joseph M
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          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
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              Value: 36
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              Value: 3
          Titles:
            – TitleFull: Journal of Logic & Computation
              Type: main
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