Unprovability of circuit upper bounds in Cook's theory PV
Jan Krajı́ček, Igor Carboni Oliveira · Logical Methods in Computer Science · 2017
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 $L otin Size(n^k)$. Our argument is non-constructive and does not provide an explicit description of this language.