The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases - approximation variants of satisfiability and graph coloring problems. We give an almost complete classification for the class of PCSPs of the form: given a 3-uniform hypergraph that has an admissible 2-coloring, find an admissible 3-coloring, where admissibility is given by a ternary symmetric relation. The only PCSP of this sort whose complexity is left open in this work is a natural hypergraph coloring problem, where admissibility is given by the relation "if two colors are equal, then the remaining one is higher."

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对称承诺约束满足问题：超越布尔情况

承诺约束满足问题 (PCSP) 是最近引入的约束满足问题 (CSP) 的广泛推广。我们研究了一类 PCSP 的计算复杂性，超出了研究最多的案例 - 可满足性和图形着色问题的近似变体。我们对以下形式的 PCSP 类给出了一个几乎完整的分类：给定一个具有可容许 2-着色的 3-均匀超图，找到一个可容许的 3-着色，其中可容许性由三元对称关系给出。在这项工作中，唯一的这种复杂性未解决的 PCSP 是一个自然超图着色问题，其中的可接受性由关系给出，“如果两种颜色相等，那么剩下的一种颜色更高”。