Unprovability of circuit upper bounds in Cook's theory PV

Abstract

We establish unconditionally that for every integer $k\ge 1$ 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.

References in corpus (1)

• Logical strength of complexity theory and a formalization of the PCP theorem in bounded arithmetic