An Arithmetic Theory for the Poly-Time Random Functions
Computational Complexity
2023-02-08 v2 Logic in Computer Science
Abstract
We introduce a new bounded theory RS^1_2 and show that the functions which are Sigma^b_1-representable in it are precisely random functions which can be computed in polynomial time. Concretely, we pass through a class of oracle functions over string, called POR, together with the theory of arithmetic RS^1_2. Then, we show that functions computed by poly-time PTMs are arithmetically characterized by a class of probabilistic bounded formulas.
Cite
@article{arxiv.2301.12028,
title = {An Arithmetic Theory for the Poly-Time Random Functions},
author = {Melissa Antonelli and Ugo Dal Lago and Davide Davoli and Isabel Oitavem and Paolo Pistone},
journal= {arXiv preprint arXiv:2301.12028},
year = {2023}
}
Comments
37 pages, pre-print