The classifications of temporal and phylogeny constraint languages stand among the most seminal complexity classifications within infinite-domain Constraint Satisfaction Problems (CSPs), yet remain the most mysterious in terms of algorithms and algebraic invariants for the tractable cases. We show that those languages which do not pp-construct EVERYTHING (and thus by the classifications 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 and phylogeny 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. Although temporal and phylogeny constraint languages appear to follow fundamentally different algorithmic principles, our proofs reveal a common core and proceed along strikingly similar lines.

翻译：时间约束语言与系统发育约束语言的分分类法，是无限域约束满足问题（CSPs）中最具开创性的复杂性分类之一，但其可解情形下的算法与代数不变量仍最为神秘。我们证明，那些不能pp-构造一切（因而根据分类法可在多项式时间内求解）的语言，实际上具有极有限的可表达能力——可通过它们pp-解释的图与超图来度量。这种局限性不仅衍生出许多此前未知的代数推论，也为此前已知的不变性提供了统一的新证明。特别地，我们证明此类时间约束语言与系统发育约束语言承认$4$元伪Siggers同态——这一结果支撑了此类同态存在性可能推广至更广泛的Bodirsky-Pinsker猜想框架。尽管时间约束语言与系统发育约束语言表面上遵循截然不同的算法原理，我们的证明却揭示了共同核心，并沿惊人相似的路径展开。