We define a class of algebras, the semilattices of Mal'cev blocks (for short, SMB algebras). In a nutshell, these algebras are semilattices in which each element gets blown up into a Mal'cev algebra. We publish for the first time our old proofs that some SMB algebras induce tractable templates of the reprove that the Constraint Satisfaction Problem. Next, we reprove that, in fact, all SMB algebras induce tractable templates of the Constraint Satisfaction Problem, a result already proved by A. Bulatov. Also, we compare the two general proofs of the CSP Dichotomy and prove they are more similar than initially thought when they are applied to SMB algebras. This paper is the second in the series of papers investigating the SMB algebras and it is a precursor to our further research on the similarities between the proofs of the Dichotomy Theorem.

翻译：定义了一类代数——Mal'cev块半格（简称SMB代数）。简而言之，这些代数是在半格结构的基础上，将每个元素膨胀为一个Mal'cev代数。我们首次公开发表了早期证明：某些SMB代数可导出约束满足问题的易处理模板。随后，我们重新证明了实际上所有SMB代数均能导出约束满足问题的易处理模板——该结果已由A. Bulatov证明。此外，我们比较了CSP二分性定理的两种通用证明，并证明了当应用于SMB代数时，这两种证明的相似性远超最初设想。本文是SMB代数系列研究的第二篇论文，也是我们进一步探索二分性定理证明之间相似性研究的前导性工作。