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

@inproceedings{Dose2019NPCompletenessPS, title={NP-Completeness, Proof Systems, and Disjoint NP-Pairs}, author={Titus Dose and Christian Gla{\ss}er}, booktitle={Electron. Colloquium Comput. Complex.}, year={2019} }

The article investigates the relation between three well-known hypotheses. Hunion: the union of disjoint ≤m-complete sets for NP is ≤m-complete Hopps: there exist optimal propositional proof systems Hcpair: there exist ≤pp m -complete disjoint NP-pairs The following results are obtained: The hypotheses are pairwise independent under relativizable proofs, except for the known implication Hopps ⇒ Hcpair. An answer to Pudlák’s question for an oracle relative to which ¬Hcpair, ¬Hopps, and UP has ≤m… Expand

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