Algebraic and algorithmic synergies between promise and infinite-domain CSPs

TL;DR

This paper develops a framework linking infinite-domain CSPs and promise CSPs, leading to new algebraic NP-hardness criteria and insights into tractability, with applications to temporal CSPs.

Contribution

It introduces a novel framework for transferring results between infinite-domain CSPs and promise CSPs, revealing new complexity criteria and connections.

Findings

New algebraic NP-hardness criteria for infinite-domain CSPs

Existence of promise CSPs with finite templates reducing to infinite-domain CSPs but not finitely tractable

Polynomial-time algorithms for temporal constraint satisfaction problems

Abstract

We establish a framework that allows us to transfer results between some constraint satisfaction problems with infinite templates and promise constraint satisfaction problems. On the one hand, we obtain new algebraic results for infinite-domain CSPs giving new criteria for NP-hardness. On the other hand, we show the existence of promise CSPs with finite templates that reduce naturally to tractable infinite-domain CSPs within the scope of the Bodirsky-Pinsker conjecture, but that are not finitely tractable, thereby showing a non-trivial connection between those two fields of research. In an important part of our proof, we also obtain uniform polynomial-time algorithms solving temporal constraint satisfaction problems.