IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i21p3429-d1511928.html
   My bibliography  Save this article

Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem

Author

Listed:
  • Andrey Nechesov

    (The Artificial Intelligence Research Center of Novosibirsk State University, Novosibirsk 630090, Russia
    These authors contributed equally to this work.)

  • Sergey Goncharov

    (Department of Discrete Mathematics and Computer Science, Novosibirsk State University, Novosibirsk 630090, Russia
    These authors contributed equally to this work.)

Abstract

In this work, a functional variant of the polynomial analogue of Gandy’s fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of recursive functions does not exceed polynomial bounds. This opens up opportunities to enhance the expressivity of p-complete languages by incorporating recursively defined constructs. This approach is particularly relevant in the following areas: AI-driven digital twins of smart cities and complex systems, trustworthy AI, blockchains and smart contracts, transportation, logistics, and aerospace. In these domains, ensuring the reliability of inductively definable processes is crucial for maintaining human safety and well-being.

Suggested Citation

  • Andrey Nechesov & Sergey Goncharov, 2024. "Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem," Mathematics, MDPI, vol. 12(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3429-:d:1511928
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/21/3429/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/21/3429/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3429-:d:1511928. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.