No-Rainbow Problem and the Surjective Constraint Satisfaction Problem

The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints, where a surjective assignment is an assignment containing all elements of the domain. In this paper we show that...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 7
Main Author: Zhuk, Dmitriy
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Computational complexity
Computer science
Online Access:Get full text
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Summary:The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints, where a surjective assignment is an assignment containing all elements of the domain. In this paper we show that the most famous SCSP, called No-Rainbow Problem, is NP-Hard. Additionally, we disprove the conjecture saying that the SCSP over a constraint language Γ and the CSP over the same language with constants have the same computational complexity up to poly-time reductions. Our counter-example also shows that the complexity of the SCSP cannot be described in terms of polymorphisms of the constraint language.
DOI:10.1109/LICS52264.2021.9470632