Deciding absorption in relational structures

TL;DR

This paper establishes a key equivalence between two concepts of absorption in finite algebras and demonstrates that it is decidable to determine whether a subset is an absorbing subuniverse in the context of relational structures.

Contribution

It proves the equivalence of absorbing and Jónsson absorbing subuniverses in finite, finitely related algebras and shows the decidability of identifying absorbing subuniverses.

Findings

Equivalence of absorbing and Jónsson absorbing subuniverses in finite algebras

Decidability of recognizing absorbing subuniverses in relational structures

Simplification of analysis of polymorphism algebras

Abstract

We prove that for finite, finitely related algebras the concepts of an absorbing subuniverse and a J\'onsson absorbing subuniverse coincide. Consequently, it is decidable whether a given subset is an absorbing subuniverse of the polymorphism algebra of a given relational structure.