The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the Dichotomy Conjecture has been proved in 2017 independently by Bulatov and Zhuk. At about the same time, a vast generalisation of CSP, called promise CSP, has started to gain prominence. In this survey, we explain the importance of promise CSP and highlight many new very interesting features that the study of promise CSP has brought to light. The complexity classification quest for the promise CSP is wide open, and we argue that, despite the promise CSP being more general, this quest is rather more accessible to a wide range of researchers than the dichotomy-led study of the CSP has been.
翻译:以Feder-Vardi Dichotomy Dichotomy Conjecture为核心的制约满意度问题的复杂性研究(CSP)在过去二十年中一直非常突出。经过长期一致的努力和许多部分结果,Bulatov和Zhuk在2017年独立证明了Dichotomis Conjecture。与此同时,CSP的广泛普及(称为承诺CSP)开始受到重视。在本次调查中,我们解释了承诺CSP的重要性,并强调了承诺研究所揭示的许多令人感兴趣的新特征。对CSP的复杂分类研究是广泛的,对承诺CSP的追求是开放的,我们争辩说,尽管CSP的承诺更为笼统,但这一探索对于广泛的研究人员来说要比CSP的二分法研究更容易获得。