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.ICALP.2020.17
URN: urn:nbn:de:0030-drops-124241
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12424/
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Brandts, Alex ; Wrochna, Marcin ; Živný, Stanislav

The Complexity of Promise SAT on Non-Boolean Domains

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Abstract

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and Håstad [FOCS'14/SICOMP'17] proved a result known as "(2+ε)-SAT is NP-hard". They showed that the problem of distinguishing k-CNF formulas that are g-satisfiable (i.e. some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if g/k < 1/2 and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus we give a dichotomy for a natural fragment of promise constraint satisfaction problems (PCSPs) on arbitrary finite domains.

BibTeX - Entry

@InProceedings{brandts_et_al:LIPIcs:2020:12424,
  author =	{Alex Brandts and Marcin Wrochna and Stanislav Živn{\'y}},
  title =	{{The Complexity of Promise SAT on Non-Boolean Domains}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12424},
  URN =		{urn:nbn:de:0030-drops-124241},
  doi =		{10.4230/LIPIcs.ICALP.2020.17},
  annote =	{Keywords: promise constraint satisfaction, PCSP, polymorphisms, algebraic approach, label cover}
}

Keywords: promise constraint satisfaction, PCSP, polymorphisms, algebraic approach, label cover
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020


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