Unprovability of circuit upper bounds in Cook's theory PV
Abstract
We establish unconditionally that for every integer $k \geq 1$ there is a language $L \in \mbox{P}$ such that it is consistent with Cook's theory PV that $L \notin Size(n^k)$. Our argument is non-constructive and does not provide an explicit description of this language.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2016
- DOI:
- 10.48550/arXiv.1605.00263
- arXiv:
- arXiv:1605.00263
- Bibcode:
- 2016arXiv160500263K
- Keywords:
-
- Mathematics - Logic;
- Computer Science - Computational Complexity;
- 03F30;
- 68Q15;
- F.4.1
- E-Print:
- Logical Methods in Computer Science, Volume 13, Issue 1 (February 3, 2017) lmcs:3119