License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.45
URN: urn:nbn:de:0030-drops-168435
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16843/
Ehrmanntraut, Anton ;
Egidy, Fabian ;
Glaßer, Christian
Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP
Abstract
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.
BibTeX - Entry
@InProceedings{ehrmanntraut_et_al:LIPIcs.MFCS.2022.45,
author = {Ehrmanntraut, Anton and Egidy, Fabian and Gla{\ss}er, Christian},
title = {{Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {45:1--45:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16843},
URN = {urn:nbn:de:0030-drops-168435},
doi = {10.4230/LIPIcs.MFCS.2022.45},
annote = {Keywords: computational complexity, promise classes, proof complexity, complete sets, oracle construction}
}
Keywords: |
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computational complexity, promise classes, proof complexity, complete sets, oracle construction |
Collection: |
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47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) |
Issue Date: |
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2022 |
Date of publication: |
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22.08.2022 |