Polymorphisms, and How to Use Them Page 1 Polymorphisms, and How to Use Them Libor Barto
∗1, Andrei Krokhin2, and Ross Willard †3 1 Department of Algebra, Faculty of Mathematics and …

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a
fixed template is that pp-interpretations between at most countable ω-categorical relational …

We prove that an ω-categorical core structure primitively positively interprets all finite
structures with parameters if and only if some stabilizer of its polymorphism clone has a …

Tame congruence theory identifies six Maltsev conditions associated with locally finite
varieties omitting certain types of local behaviour. Extending a result of Siggers, we show …

The tractability conjecture for finite domain constraint satisfaction problems (CSPs) stated
that such CSPs are solvable in polynomial time whenever there is no natural reduction, in …

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a
set of constraints on the variables, whether or not there is an assignment to the variables …

The algebraic approach to Constraint Satisfaction Problem led to many developments in
both CSP and universal algebra. The notion of absorption was successfully applied on both …

An equational condition is a set of equations in an algebraic language, and an algebraic
structure satisfies such a condition if it possesses terms that meet the required equations …

These are notes from a multi-year learning seminar on the algebraic approach to Constraint
Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures …

We survey recent results on the broad family of problems that can be cast as valued
constraint satisfaction problems (VCSPs). We discuss general methods for analysing the …