发表机构
Toronto Metroplitan University（多伦多都会大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明具有Maltsev同态的有限关系模板的CSP问题属于复杂度类DET，并提出一种新算法，该算法利用2生成子代数图而非显式同态，将问题与带计数的确定性对数空间联系起来。
AI 中文摘要
在本文中，我们证明了求解CSP(A)的问题属于一个特定的复杂度类DET，其中A是一个有限关系模板，且该模板承认一个Maltsev同态。DET类与计算整数矩阵行列式的复杂度相关，并与计算复杂度理论中已被充分研究的MOD-对数空间类密切相关。为证明这一事实，我们开发了一种新算法，用于求解语法上简单的二元Maltsev约束满足问题实例，该算法与著名的Bulatov-Dalmau算法截然不同。该算法不需要显式使用或知道模板的Maltsev同态，而是利用一个图，其顶点是A的2生成子代数，其中A是参数化CSP(A)的Maltsev代数。该算法的理论重要性体现在两个事实上：(1)它将问题CSP(A)置于一个与带计数的确定性对数空间相关的复杂度类中，而该复杂度类本身与线性代数中的多种标准算法问题有紧密联系；(2)它仅利用模板的关系结构，无需显式使用相容的Maltsev同态，完全依赖于与这类同态相容的约束的强“对称性”以及对A的2生成子代数的了解。
英文摘要
In this article, we prove that the problem of solving $\operatorname{CSP}(\mathbf{A})$, where $\mathbf{A}$ is a finite relational template which admits a Maltsev polymorphism is in a specific complexity class DET, which is related to the complexity of computing the determinant of a matrix with integer entries. Such a class is intimately related to well-studied MOD-logspace classes in the theory of computational complexity. To prove this fact, we develop a new algorithm for solving syntactically simple binary instances of Maltsev constraint satisfaction problems, rather different from the well-known Bulatov-Dalmau algorithm, which does not require the explicit use or knowledge of a Maltsev polymorphism of the template but, rather, utilizes a graph whose vertices are 2-generated subuniverses of $\mathbb{A}$, where $\mathbb{A}$ is the Maltsev algebra parametrizing $\operatorname{CSP}(\mathbf{A})$. The theoretical importance of this algorithm is reflected in two facts: (1) it places the problem $ \operatorname{CSP}(\mathbf{A})$ in a complexity class related to the deterministic logspace with counting, which, in itself, has a strong connection to a variety of standard algorithmic problems in linear algebra, and (2) it only makes use of the relational structure of the template without the need for the explicit use of a compatible Maltsev polymorphism, depending entirely on the strong ``symmetry" of constraints compatible with such polymorphisms and the knowledge of 2-generated subuniverses of $\mathbb{A}$.
