An invitation to the promise constraint satisfaction problem

TL;DR

This paper surveys the promise constraint satisfaction problem (promise CSP), emphasizing its significance, recent developments, and the open complexity classification challenges, highlighting its accessibility compared to traditional CSP studies.

Contribution

It provides an overview of promise CSP, discusses its importance, recent progress, and argues that its complexity classification is more approachable for researchers.

Findings

The promise CSP has gained prominence as a generalization of CSP.

The Dichotomy Conjecture for CSP was proven in 2017 by Bulatov and Zhuk.

The complexity classification for promise CSP remains an open problem.

Abstract

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.