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Complexity of inverse constraint problems and a dichotomy for the inverse satisfiability problem
Journal of Computer and System Sciences ( IF 1.1 ) Pub Date : 2020-11-18 , DOI: 10.1016/j.jcss.2020.10.004
Victor Lagerkvist , Biman Roy

The inverse satisfiability problem over a set of relations Γ (Inv-SAT(Γ)) is the problem of deciding whether a relation R can be defined as the set of models of a SAT(Γ) instance. Kavvadias and Sideri (1998) [15] obtained a dichotomy between P and co-NP-complete for finite Γ containing the two constant Boolean relations. However, for arbitrary constraint languages the complexity has been wide open, and in this article we finally prove a complete dichotomy theorem for finite languages. Kavvadias and Sideri's techniques are not applicable and we have to turn to the more recent algebraic approach based on partial polymorphisms. We also study the complexity of the inverse constraint satisfaction problem prove a general hardness result, which in particular resolves the complexity of inverse k-colouring, mentioned as an open problem in Chen (2008) [8].



中文翻译:

反约束问题的复杂性和反可满足性问题的二分法

逆满足性问题在一组关系的Γ(INV-SAT(Γ))是决定一个关系是否问题- [R可以被定义为一组的一个的模型SAT(Γ)实例。Kavvadias和Sideri(1998)[15]对包含两个常数布尔关系的有限Γ获得了P和共NP-完全之间的二分法。但是,对于任意约束语言,其复杂性已广为接受,在本文中,我们最终证明了有限语言的完整二分定理。Kavvadias和Sideri的技术不适用,我们不得不转向基于局部多态性的最新代数方法。我们还研究了逆的复杂性约束满足问题证明了一般的硬度结果,特别是解决了 k着色的复杂性,在Chen(2008)[8]中被称为开放问题。

更新日期:2020-11-21
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