Research output: Contribution to journal › Article › peer-review
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
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TY - JOUR
T1 - Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem
AU - Nechesov, Andrey
AU - Goncharov, Sergey
N1 - This work was supported by a grant for research centers, provided by the Analytical Center for the Government of the Russian Federation in accordance with the subsidy agreement (agreement identifier 000000D730324P540002) and the agreement with the Novosibirsk State University dated 27 December 2023 No. 70-2023-001318. Nechesov, A. Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem / A. Nechesov, S. Goncharov // Mathematics. – 2024. – Vol. 12, No. 21. – P. 3429. – DOI 10.3390/math12213429.
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/
UR - https://www.elibrary.ru/item.asp?id=79075715
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