Understanding the computational complexity of fragments of the Constraint Satisfaction Problem (CSP) has been instrumental in the formulation of Feder-Vardi's Dichotomy Conjecture and its positive resolution by Bulatov and Zhuk. An approximation version of the CSP - known as the promise CSP - has recently gained prominence as an exciting generalisation of the CSP that captures many fundamental computational problems. In this work, we establish a computational complexity dichotomy for a natural fragment of the promise CSP consisting of homomorphism problems involving a class of 3-uniform hypergraphs.

翻译：理解约束满足问题（CSP）片段的计算复杂性对于Feder-Vardi二分猜想的确立以及Bulatov与Zhuk对该猜想的肯定性解决起到了关键作用。CSP的一个近似版本——即承诺CSP——近年来因作为CSP激动人心的推广形式并涵盖众多基础计算问题而备受关注。在本工作中，我们针对承诺CSP的一个自然片段（包含一类3一致超图的同态问题）建立了计算复杂性二分定理。