Semigroups and one-way functions
Group Theory
2015-03-09 v3 Computational Complexity
Abstract
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular semigroup. The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are the non-regular elements of fP. We prove various properties of fP, e.g., that it is finitely generated. We define reductions with respect to which certain universal one-way functions are fP-complete.
Cite
@article{arxiv.1306.1447,
title = {Semigroups and one-way functions},
author = {J. C. Birget},
journal= {arXiv preprint arXiv:1306.1447},
year = {2015}
}
Comments
25 pages. This 3rd version benefitted from referee comments in International J. of Algebra and Computation, 2015