# P-Optimal Proof Systems for Each Set in coNP and no Complete Problems in NP⋂coNP Relative to an Oracle

@article{Dose2019POptimalPS, title={P-Optimal Proof Systems for Each Set in coNP and no Complete Problems in NP⋂coNP Relative to an Oracle}, author={Titus Dose}, journal={ArXiv}, year={2019}, volume={abs/1910.08571} }

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$\mathrm{P}\ne\mathrm{NP}$ 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

NP-Completeness, Proof Systems, and Disjoint NP-Pairs

- Mathematics, Computer Science
- Electron. Colloquium Comput. Complex.
- 2019

The article investigates the relation between three well-known hypotheses, Hunion, Hopps and Hcpair, and characterizations of Hunion and two variants in terms of coNP-completeness and pproducibility of the set of hard formulas of propositional proof systems are obtained. Expand