Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish between whether a given instance of a CSP has a solution or not even a specified relaxation can be satisfied. All currently known tractable PCSPs can be reduced in a natural way to tractable CSPs. Barto arXiv:1909.04878 presented an example of a PCSP over Boolean structures for which this reduction requires solving a CSP over an infinite structure. We give a first example of a PCSP over Boolean structures which reduces to a tractable CSP over a structure of size $3$ but not smaller. Further we investigate properties of PCSPs that reduce to systems of linear equations or to CSPs over structures with semilattice or majority polymorphism.

中文翻译：

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Promise 约束满足的三明治

Promise Constraint Satisfaction Problems (PCSP) 最近由 Brakensiek 和 Guruswami arXiv:1704.01937 提出，作为研究约束满足问题 (CSP) 近似的框架。非正式地，PCSP 要求区分给定的 CSP 实例是否有解决方案，或者甚至不能满足指定的松弛。所有目前已知的易处理 PCSP 都可以以自然的方式减少到易处理的 CSP。Barto arXiv:1909.04878 展​​示了一个基于布尔结构的 PCSP 示例，对于这种简化需要解决一个无限结构上的 CSP。我们给出了布尔结构上的 PCSP 的第一个示例，该示例在大小为 $3$ 但不更小的结构上简化为易于处理的 CSP。