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Beyond PCSP(1-in-3,NAE)

Abstract:

The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of each constraint: a strict one and a weak one. Given the promise that a solution exists using the strict constraints, the task is to find a solution using the weak constraints. While there are by now several dichotomy results for fragments of PCSPs, they all consider (in some way) symmetric PCSPs.

1-in-3-SAT and Not-All-Equal-3-SAT are classic examples of Boolean symmetric (non-promise) CSPs. While both problems are NP-hard, Brakensiek and Guruswami showed [SODA'18] that given a satisfiable instance of 1-in-3-SAT one can find a solution to the corresponding instance of (weaker) Not-All-Equal-3-SAT. In other words, the PCSP template (𝟏-in-𝟑,NAE) is tractable.

We focus on non-symmetric PCSPs. In particular, we study PCSP templates obtained from the Boolean template (𝐭-in-𝐤, NAE) by either adding tuples to 𝐭-in-𝐤 or removing tuples from NAE. For the former, we classify all templates as either tractable or not solvable by the currently strongest known algorithm for PCSPs, the combined basic LP and affine IP relaxation of Brakensiek and Guruswami [SODA'20]. For the latter, we classify all templates as either tractable or NP-hard.

Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4230/LIPIcs.ICALP.2021.121

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
ORCID:
0000-0002-0263-159X


Publisher:
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages:
121:1–121:14
Series:
Leibniz International Proceedings in Informatics
Series number:
198
Place of publication:
Germany
Publication date:
2021-07-02
Acceptance date:
2021-04-22
Event title:
48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Event location:
Online (Glasgow, Scotland)
Event website:
http://easyconferences.eu/icalp2021/
Event start date:
2021-07-12
Event end date:
2021-07-16
DOI:
ISSN:
1868-8969
ISBN:
9783959771955


Language:
English
Keywords:
Pubs id:
1173839
Local pid:
pubs:1173839
Deposit date:
2021-04-26

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