发表机构
Indian Institute of Science Education and Research (IISER) Pune（印度科学教育研究所浦那分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对通用代数中有限相关克隆的判定问题，证明有限域上的克隆及其n元部分的作用代数有限相关等价，并应用自然克隆同构得到有限代数与其足够秩自由代数有限相关的等价结论。
AI 中文摘要
约束满足问题（CSP）为表达复杂的算法决策问题提供了框架。对于有限域CSP，多态克隆是支配相关约束语言的基础代数不变量。通用代数中的一个基础结构问题是如何判定给定克隆是否为有限相关的。本文证明，有限域C上的克隆$\boldsymbol{\textit{C}}$是有限相关的，当且仅当它在其n元部分（$n \boldsymbol{\textit{\textgreater}}= |C|$）上的作用代数$\boldsymbol{\textit{\tilde{C}} = \textit{C} \boldsymbol{\textit{\textcurlywedge}} \textit{C}^{(n)}}$是有限相关的。随后，我们应用自然克隆同构证明，有限代数是有限相关的，当且仅当它具有足够秩的自由代数是有限相关的。
英文摘要
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.
Comments12 pages
