## Jan Krajicek ; Igor C. Oliveira - Unprovability of circuit upper bounds in Cook's theory PV

lmcs:3119 - Logical Methods in Computer Science, February 3, 2017, Volume 13, Issue 1 - https://doi.org/10.23638/LMCS-13(1:4)2017
Unprovability of circuit upper bounds in Cook's theory PV

Authors: Jan Krajicek ; Igor C. Oliveira

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.

Volume: Volume 13, Issue 1
Published on: February 3, 2017
Accepted on: February 3, 2017
Submitted on: February 3, 2017
Keywords: Mathematics - Logic,Computer Science - Computational Complexity,03F30, 68Q15,F.4.1