We provide a unified framework to study hierarchies of relaxations for Constraint Satisfaction
Problems and their Promise variant. The idea is to split the description of a hierarchy into an …

We introduce the novel machinery of smooth approximations, and apply it to confirm the
CSP dichotomy conjecture for first-order reducts of the random tournament, and to give new …

We study the complexity of infinite-domain constraint satisfaction problems (CSPs): our basic
setting is that a complexity classification for the CSPs of first-order expansions of a structure …

A Constraint Satisfaction Problem (CSP) is a computational problem where we are given
variables and constraints about them; the question is whether the variables can be assigned …

For a fixed finite set of finite tournaments ${\mathcal F} $, the ${\mathcal F} $-free orientation
problem asks whether a given finite undirected graph $ G $ has an $\mathcal F $-free …

We introduce the novel machinery of smooth approximations to provide a systematic
algebraic approach to the complexity of CSPs over finitely bounded homogeneous …

Two particularly active branches of research in constraint satisfaction are the study of
promise constraint satisfaction problems (PCSPs) with finite templates and the study of …

We investigate thelocal consistency implies global consistency'principle of strict width
among structures within the scope of the Bodirsky-Pinsker dichotomy conjecture for infinite …

We study the Sherali-Adams linear programming hierarchy in the context of promise
constraint satisfaction problems (PCSPs). We characterise when a level of the hierarchy …

We prove that relational structures admitting specific polymorphisms (namely, canonical
pseudo-WNU operations of all arities $ n\geq 3$) have low relational width. This implies a …