An Application of Farkas' Lemma to Finite-Valued Constraint Satisfaction Problems over Infinite Domains

TL;DR

This paper explores the expressive power of finite-valued constraint satisfaction problems over infinite domains using algebraic methods, providing a universal characterization.

Contribution

It introduces a universal algebraic local characterization of the expressive power of finite-valued languages over infinite domains.

Findings

Provides a universal algebraic local characterization

Applies to languages with arbitrary cost functions and domain sizes

Advances understanding of constraint satisfaction over infinite domains

Abstract

We show a universal algebraic local characterisation of the expressive power of finite-valued languages with domains of arbitrary cardinality and containing arbitrary many cost functions.