Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami (SODA’20) for promise (non-valued) CSPs (on finite domains).

中文翻译：

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无限域上 Promise VCSP 的基本 LP 和仿射 IP 放宽组合

凸松弛有助于约束满足问题 (CSP) 的可解性，以及 CSP 的三种不同概括：值 CSP、无限域 CSP 和最近的承诺 CSP。在这项工作中，我们将现有的易处理性结果扩展到组合 CSP 的三个推广：我们为组合基本线性规划和仿射整数规划松弛给出了充分条件，以实现在无限域上的承诺值 CSP 的精确可解性。这扩展了 Brakensiek 和 Guruswami (SODA'20) 的结果，用于承诺（非值）CSP（在有限域上）。