An invitation to the promise constraint satisfaction 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.

arXiv commentThis survey appeared in ACM SIGLOG News, Volume 9, Issue 3, July 2022, pp 30-59, https://doi.org/10.1145/3559736.3559740

References in corpus (8)

• Algebraic approach to promise constraint satisfaction
• The Power of the Combined Basic LP and Affine Relaxation for Promise CSPs
• The complexity of promise SAT on non-Boolean domains
• Conditional Dichotomy of Boolean Ordered Promise CSPs
• Beyond PCSP (1-in-3,NAE)
• A note on hardness of promise hypergraph colouring
• Small Promise CSPs that reduce to large CSPs
• The Sherali-Adams Hierarchy for Promise CSPs through Tensors

Cited by in corpus (2)

• Local consistency as a reduction between constraint satisfaction problems
• On the complexity of symmetric vs. functional PCSPs