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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无限域上承诺 VCSP 的组合基本 LP 和仿射 IP 松弛

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：有价值的 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 CSP 组合的三个概括：我们为组合基本线性规划和仿射整数规划松弛提供了充分条件，以实现无限域上承诺值 CSP 的精确可解性。这扩展了 Brakensiek 和 Guruswami [SODA'20] 对于承诺（非价值）CSP（在有限域上）的结果。