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When Darwin Met Ianus: Dichotomies of Expressivity

Authors Johanna Brunar , Michael Pinsker , Moritz Schöbi

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LIPIcs.MFCS.2026.100.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Constraint Satisfaction Problem (CSP)
  • Temporal Constraint language
  • Phylogeny Constraint language
  • pseudo-loop
  • primitive positive interpretation
  • polymorphism
  • oligomorphic permutation group
  • identity

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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!"

Cite As Get BibTex

Johanna Brunar, Michael Pinsker, and Moritz Schöbi. When Darwin Met Ianus: Dichotomies of Expressivity. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 100:1-100:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.100

Author Details

Johanna Brunar
  • TU Wien, Austria
Michael Pinsker
  • TU Wien, Austria
Moritz Schöbi
  • TU Wien, Austria

Funding

Funded by the European Union (ERC, POCOCOP, 101071674). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This research was funded in whole or in part by the Austrian Science Fund (FWF) [I5948]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. The first author is a recipient of a DOC Fellowship of the Austrian Academy of Sciences at Technische Universität Wien.

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