Finite Relation Algebras with Normal Representations

TL;DR

This paper explores finite relation algebras with normal representations, translating recent constraint satisfaction complexity results into the relation algebra framework and highlighting open problems at the intersection of model theory and relation algebras.

Contribution

It bridges recent advances in infinite-domain constraint satisfaction problems with the traditional relation algebra setting, identifying new open research questions.

Findings

Relation algebra approach can incorporate recent complexity results.

Normal representations in relation algebras relate to constraint satisfaction complexity.

Open problems connect model theory and relation algebra theory.

Abstract

One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research challenges of this application field. The past decade has brought significant progress on the theory of constraint satisfaction, both over finite and infinite domains. This progress has been achieved independently from the relation algebra approach. The present article translates the recent findings into the traditional relation algebra setting, and points out a series of open problems at the interface between model theory and the theory of relation algebras.