Year: 2026
Type: preprint
Abstract: 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. When Ianus can't express it all He tries in vain, he hits a wall When for 𝕂₃ no way he knows His face of pseudo-loops he shows. As Darwin finds such twisted edge To pines and vines he makes this pledge: "Should free of pseudo-loops you shine All finite structures shall be thine!"
Source: arXiv (Cornell University)
Institution: TU Wien
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7080182359
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