License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2020.9
URN: urn:nbn:de:0030-drops-118707
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11870/
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Dose, Titus ; Glaßer, Christian

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

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LIPIcs-STACS-2020-9.pdf (0.5 MB)

Abstract

The article investigates the relation between three well-known hypotheses.
- H_{union}: the union of disjoint ≤^p_m-complete sets for NP is ≤^p_m-complete
- H_{opps}: there exist optimal propositional proof systems
- H_{cpair}: 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 H_{opps} ⇒ H_{cpair}.
- An answer to Pudlák’s question for an oracle relative to which ¬H_{cpair}, ¬H_{opps}, and UP has ≤^p_m-complete sets.
- The converse of Köbler, Messner, and Torán’s implication NEE ∩ TALLY ⊆ coNEE ⇒ H_{opps} fails relative to an oracle, where NEE =^{df} NTIME(2^O(2ⁿ)).
- New characterizations of H_{union} and two variants in terms of coNP-completeness and p-producibility of the set of hard formulas of propositional proof systems.

BibTeX - Entry

@InProceedings{dose_et_al:LIPIcs:2020:11870,
  author =	{Titus Dose and Christian Gla{\ss}er},
  title =	{{NP-Completeness, Proof Systems, and Disjoint NP-Pairs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11870},
  URN =		{urn:nbn:de:0030-drops-118707},
  doi =		{10.4230/LIPIcs.STACS.2020.9},
  annote =	{Keywords: NP-complete, propositional proof system, disjoint NP-pair, oracle}
}

Keywords: NP-complete, propositional proof system, disjoint NP-pair, oracle
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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