English

Unprovability of circuit upper bounds in Cook's theory PV

Logic 2017-02-15 v3 Computational Complexity

Abstract

We establish unconditionally that for every integer k1k \geq 1 there is a language L\mboxPL \in \mbox{P} such that it is consistent with Cook's theory PV that LSize(nk)L \notin Size(n^k). Our argument is non-constructive and does not provide an explicit description of this language.

Keywords

Cite

@article{arxiv.1605.00263,
  title  = {Unprovability of circuit upper bounds in Cook's theory PV},
  author = {Jan Krajicek and Igor C. Oliveira},
  journal= {arXiv preprint arXiv:1605.00263},
  year   = {2017}
}