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

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Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem. / Nechesov, Andrey ; Goncharov, Sergey.

In: Mathematics, Vol. 12, No. 21, 3429, 11.2024.

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

BibTeX

@article{c3c9bfa628784cceb708c16ae7375923,

title = "Functional Variant of Polynomial Analogue of Gandy{\textquoteright}s Fixed Point Theorem",

abstract = "In this work, a functional variant of the polynomial analogue of Gandy{\textquoteright}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.",

keywords = "Gandy{\textquoteright}s fixed point theorem, artificial intelligence, polynomial computability, smart cities",

author = "Andrey Nechesov and Sergey Goncharov",

year = "2024",

month = nov,

doi = "10.3390/math12213429",

language = "English",

volume = "12",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "21",

}

RIS

TY - JOUR

T1 - Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem

AU - Nechesov, Andrey

AU - Goncharov, Sergey

PY - 2024/11

Y1 - 2024/11

N2 - 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.

AB - 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.

KW - Gandy’s fixed point theorem

KW - artificial intelligence

KW - polynomial computability

KW - smart cities

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85208579601&origin=inward&txGid=8b414f3ae70f6b72019d5b9d6b197523

UR - https://www.mendeley.com/catalogue/6f4f6de9-8c1d-3abb-a471-b1d30667b74d/

U2 - 10.3390/math12213429

DO - 10.3390/math12213429

M3 - Article

VL - 12

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 21

M1 - 3429

ER -

ID: 61105741