On the consistency of stronger lower bounds for NEXP
Logic in Computer Science
2025-11-26 v4 Computational Complexity
Logic
Abstract
It was recently shown by Atserias, Buss and Mueller that the standard complexity-theoretic conjecture NEXP not in P / poly is consistent with the relatively strong bounded arithmetic theory V^0_2, which can prove a substantial part of complexity theory. We observe that their approach can be extended to show that the stronger conjectures NEXP not in EXP / poly and NEXP not in coNEXP are consistent with a stronger theory, which includes every true universal number-sort sentence.
Cite
@article{arxiv.2504.03320,
title = {On the consistency of stronger lower bounds for NEXP},
author = {Neil Thapen},
journal= {arXiv preprint arXiv:2504.03320},
year = {2025}
}