一句话：提出通用代数新方法，用于攻克小代数CSP分类难题，并证明基数≤4的交换幂等二元代数对应CSP可处理。
过去十五年，代数CSP二分猜想取得重大进展，其核心命题是：与有限幂等代数相关的每个局部约束满足问题可处理，当且仅当该代数具有Taylor项运算。尽管已有包括一般猜想证明在内的成果，一些仅含单个二元运算的小代数，其CSP仍难以用已知方法直接判定为可处理或NP完全。本文提出若干新方法，重点针对称为“交换幂等二元代数”（CIB）的有限代数类。作者利用这些方法证明，基数不超过4的每个CIB所对应的CSP都是可处理的。
After substantial progress over the last 15 years, the "algebraic CSP-dichotomy conjecture" reduces to the following: every local constraint satisfaction problem (CSP) associated with a finite idempotent algebra is tractable if and only if the algebra has a Taylor term operation. Despite the tremendous achievements in this area (including recently announce proofs of the general conjecture), there remain examples of small algebras with just a single binary operation whose CSP resists direct classification as either tractable or NP-complete using known methods. In this paper we present some new methods for approaching such problems, with particular focus on those techniques that help us attack the class of finite algebras known as "commutative idempotent binars" (CIBs). We demonstrate the utility of these methods by using them to prove that every CIB of cardinality at most 4 yields a tractable CSP.
@article{paperbot1739,
title = {Universal Algebraic Methods for Constraint Satisfaction Problems},
author = {Clifford Bergman and William DeMeo},
journal = {Logical Methods in Computer Science},
volume = {Volume 18, Issue 1},
year = {2022},
doi = {10.46298/lmcs-18(1:12)2022}
}