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The Complexity of Promise SAT on Non-Boolean Domains

Authors Alex Brandts, Marcin Wrochna , Stanislav Živný

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Constraint and logic programming
Keywords
  • promise constraint satisfaction
  • PCSP
  • polymorphisms
  • algebraic approach
  • label cover

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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.

Cite As Get BibTex

Alex Brandts, Marcin Wrochna, and Stanislav Živný. The Complexity of Promise SAT on Non-Boolean Domains. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.17

Author Details

Alex Brandts
  • Department of Computer Science, University of Oxford, UK
Marcin Wrochna
  • Department of Computer Science, University of Oxford, UK
Stanislav Živný
  • Department of Computer Science, University of Oxford, UK

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper reflects only the authors' views and not the views of the ERC or the European Commission. The European Union is not liable for any use that may be made of the information contained therein.
  • Brandts, Alex: Royal Society Enhancement Award and NSERC PGS Doctoral Award
  • Živný, Stanislav: Royal Society University Research Fellowship

Acknowledgements

We would like to thank the anonymous reviewers for their comments.

References

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