Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification.

中文翻译：

---

单调模式定义的 CSP 的单例弧一致性

单例弧一致性是一种重要的局部一致性类型，最近已证明它可以解决有界宽度约束语言上的所有约束满足问题 (CSP)。我们的目标是表征由禁止模式定义的所有类别的 CSP，这些模式通过单例弧一致性解决并在去除约束下关闭。我们确定了五种新模式，它们的缺失通过单例弧一致性确保了可解性，其中四种可证明是最大的，其中三种概括了 2-SAT。结合其他模式的简单反例，我们在完整分类方面取得了重大进展。