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

Andrey Nechesov () and Sergey Goncharov
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Andrey Nechesov: The Artificial Intelligence Research Center of Novosibirsk State University, Novosibirsk 630090, Russia
Sergey Goncharov: Department of Discrete Mathematics and Computer Science, Novosibirsk State University, Novosibirsk 630090, Russia

Mathematics, 2024, vol. 12, issue 21, 1-14

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.

Keywords: polynomial computability; Gandy’s fixed point theorem; artificial intelligence; smart cities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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