eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-08-22
45:1
45:15
10.4230/LIPIcs.MFCS.2022.45
article
Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP
Ehrmanntraut, Anton
1
https://orcid.org/0000-0001-6677-586X
Egidy, Fabian
1
https://orcid.org/0000-0001-8370-9717
Glaßer, Christian
1
Julius-Maximilians-Universität Würzburg, Germany
We construct an oracle relative to which P = NP ∩ coNP, but there are no many-one complete sets in UP, no many-one complete disjoint NP-pairs, and no many-one complete disjoint coNP-pairs.
This contributes to a research program initiated by Pudlák [P. Pudlák, 2017], which studies incompleteness in the finite domain and which mentions the construction of such oracles as open problem. The oracle shows that NP ∩ coNP is indispensable in the list of hypotheses studied by Pudlák. Hence one should consider stronger hypotheses, in order to find a universal one.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol241-mfcs2022/LIPIcs.MFCS.2022.45/LIPIcs.MFCS.2022.45.pdf
computational complexity
promise classes
proof complexity
complete sets
oracle construction