The existence of a near-unanimity function is decidable

TL;DR

This paper proves that it is possible to algorithmically determine whether a finite set of relations admits a near-unanimity function, addressing a fundamental question in algebra and computational logic.

Contribution

It establishes the decidability of the existence of near-unanimity functions for finite relation sets, a problem previously unresolved.

Findings

Decidability of near-unanimity function existence proven

Provides an algorithmic approach for the decision problem

Advances understanding in algebraic logic and computational complexity

Abstract

We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.