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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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
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Abstract 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.
AbstractList 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.
Author Zhuk, Dmitriy
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  organization: HSE University,Russia
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Snippet The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to...
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SubjectTerms Computational complexity
Computer science
Title No-Rainbow Problem and the Surjective Constraint Satisfaction Problem
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