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: https://drops.dagstuhl.de/opus/volltexte/2022/16843/
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Ehrmanntraut, Anton ; Egidy, Fabian ; Glaßer, Christian

Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP

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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: computational complexity, promise classes, proof complexity, complete sets, oracle construction
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022


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