English

$\mathrm{P}$-Optimal Proof Systems for Each $\mathrm{coNP}$-Complete Set and no Complete Problems in $\mathrm{NP}\cap\mathrm{coNP}$ Relative to an Oracle

Computational Complexity 2020-01-10 v2 Logic in Computer Science

Abstract

We build on a working program initiated by Pudl\'ak [Pud17] and construct an oracle relative to which each coNP\mathrm{coNP}-complete set has P\mathrm{P}-optimal proof systems and NPcoNP\mathrm{NP}\cap\mathrm{coNP} does not have complete problems.

Cite

@article{arxiv.1910.08571,
  title  = {$\mathrm{P}$-Optimal Proof Systems for Each $\mathrm{coNP}$-Complete Set and no Complete Problems in $\mathrm{NP}\cap\mathrm{coNP}$ Relative to an Oracle},
  author = {Titus Dose},
  journal= {arXiv preprint arXiv:1910.08571},
  year   = {2020}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1904.06175, arXiv:1909.02839

R2 v1 2026-06-23T11:48:08.513Z