Year: 2026
Type: preprint
Abstract: For finite-domain constraint satisfaction problems (CSPs), the polymorphism clone provides an algebraic framework for studying the associated constraint language. A central question in clone theory is whether a clone is finitely related, that is, whether it is determined by the operations preserving a finite set of relations. Here, we study this question through the action algebra of a clone on its own $n$-ary part. We prove that a clone $\mathcal{C}$ on a finite domain $C$ is finitely related if and only if its action algebra $\widetilde{\mathcal{C}} = \mathcal{C} \curvearrowright \mathcal{C}^{(n)}$ is finitely related, provided that $n \geq |C|$. We also apply natural clone isomorphisms to obtain a finite-relatedness criterion for free algebras: a finite algebra is finitely related if and only if its free algebra of sufficiently large finite rank is finitely related.
Source: arXiv (Cornell University)
Author: Tiwari, Vishwesh
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G1304993860
OpenAlex ID: W7203783571