The Bodirsky-K\'ara classification of temporal constraint languages stands as one of the earliest and most seminal complexity classifications within infinite-domain Constraint Satisfaction Problems (CSPs), yet it remains one of the most mysterious in terms of algorithms and algebraic invariants for the tractable cases. We show that those temporal languages which do not pp-construct EVERYTHING (and thus by the classification are solvable in polynomial time) have, in fact, very limited expressive power as measured by the graphs and hypergraphs they can pp-interpret. This limitation yields many previously unknown algebraic consequences, while also providing new, uniform proofs for known invariance properties. In particular, we show that such temporal constraint languages admit $4$-ary pseudo-Siggers polymorphisms -- a result that sustains the possibility that the existence of such polymorphisms extends to the much broader context of the Bodirsky-Pinsker conjecture.

翻译：Bodirsky-Kára时间约束语言分类作为无限域约束满足问题（CSPs）中最早且最具开创性的复杂性分类之一，其在可处理情形下的算法与代数不变量方面仍是最为神秘的分类体系之一。本文证明，那些不能通过pp构造生成EVERYTHING的时间语言（根据分类属于多项式时间可解类）实际上具有极其有限的表达能力——这一结论通过它们能pp解释的图与超图进行度量。这种局限性产生了许多先前未知的代数推论，同时为已知的不变性性质提供了新颖的统一证明。特别地，我们证明此类时间约束语言允许四元伪Siggers多态性——该结果支持了此类多态性存在性可扩展至更广泛的Bodirsky-Pinsker猜想背景的可能性。