Corpus ID: 212816554

# 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}
}
• Titus Dose
• Published 2019
• Mathematics, Computer Science
• arXiv: Computational Complexity
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. - $\mathsf{NP}\cap\mathsf{coNP}$: $\text{NP}\cap\text… Expand 2 Citations #### Topics from this paper$\mathrm{P}$-Optimal Proof Systems for Each$\mathrm{coNP}$-Complete Set and no Complete Problems in$\mathrm{NP}\cap\mathrm{coNP}$Relative to an Oracle. We build on a working program initiated by Pudl\'ak [Pud17] and construct an oracle relative to which each$\mathrm{coNP}$-complete set has$\mathrm{P}$-optimal proof systems andExpand$\mathrm{P}\ne\mathrm{NP}$and All Non-Empty Sets in$\mathrm{NP}\cup\mathrm{coNP}$Have P-Optimal Proof Systems Relative to an Oracle. As one step in a working program initiated by Pudlak [Pud17], an oracle is constructed relative to which P and all non-empty sets in NP have-optimal proof systems. Expand #### References SHOWING 1-10 OF 15 REFERENCES New relations and separations of conjectures about incompleteness in the finite domain It is proved that existence of a p-optimal proof system for$\mathsf{TAUT}$and existence ofA complete problem for$\ mathsf{TFNP}\$ are independent of each other in relativized worlds which was not known before. Expand
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