arXiv subjects

Johanna Brunar

Publications and source records attributed to Johanna Brunar.

2 recordsLinked to original sources

arXiv2026

When Darwin met Ianus: dichotomies of expressivity

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.

cs.LO↗

arXiv2026

The sorrows of a smooth digraph: the first hardness criterion for infinite directed graph-colouring problems

Two major milestones on the road to the full complexity dichotomy for finite-domain constraint satisfaction problems were Bulatov's proof of the dichotomy for conservative templates, and the structural dichotomy for smooth digraphs of algebraic length 1 due to Barto, Kozik, and Niven. We lift the combined scenario to the infinite, and prove that any smooth digraph of algebraic length 1 pp-constructs, together with pairs of orbits of an oligomorphic subgroup of its automorphism group, every finite structure -- and hence its conservative graph-colouring problem is NP-hard -- unless the digraph has a pseudo-loop, i.e. an edge within an orbit. We thereby overcome, for the first time, previous obstacles to lifting structural results for digraphs in this context from finite to $ω$-categorical structures; the strongest lifting results hitherto not going beyond a generalisation of the Hell-Nešetřil theorem for undirected graphs. As a consequence, we obtain a new algebraic invariant of arbitrary $ω$-categorical structures enriched by pairs of orbits which fail to pp-construct some finite structure.

cs.LO↗