# P-Optimal Proof Systems for Each NP-Complete Set but no Complete Disjoint NP-Pairs Relative to an Oracle.

@article{Dose2019POptimalPS, title={P-Optimal Proof Systems for Each NP-Complete Set but no Complete Disjoint NP-Pairs Relative to an Oracle.}, author={Titus Dose}, journal={arXiv: Computational Complexity}, year={2019} }

Pudlak [Pud17] lists several major conjectures from the field of proof complexity and asks for oracles that separate corresponding relativized conjectures. Among these conjectures are:
- $\mathsf{DisjNP}$: The class of all disjoint NP-pairs does not have many-one complete elements.
- $\mathsf{SAT}$: NP does not contain many-one complete sets that have P-optimal proof systems.
- $\mathsf{UP}$: UP does not have many-one complete problems.
- $\mathsf{NP}\cap\mathsf{coNP}$: $\text{NP}\cap\text… Expand

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

- Mathematics
- 2019

We build on a working program initiated by Pudl\'ak [Pud17] and construct an oracle relative to which each $\mathrm{coNP}$-complete set has $\mathrm{P}$-optimal proof systems and… Expand

$\mathrm{P}\ne\mathrm{NP}$ and All Non-Empty Sets in $\mathrm{NP}\cup\mathrm{coNP}$ Have P-Optimal Proof Systems Relative to an Oracle.

- Mathematics, Computer Science
- 2019

As one step in a working program initiated by Pudlak [Pud17], an oracle is constructed relative to which P and all non-empty sets in NP have-optimal proof systems. Expand

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