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cs.CG2025
Devil's Games and : Continuous Games complete for the First-Order Theory of the Reals
Lucas Meijer, Arnaud de Mesmay, Tillmann Miltzow +2
We introduce the complexity class Quantified Reals (). Let FOTR be the set of true sentences in the first-order theory of the reals. A language is in $\text…
cs.CG2020
Algorithms for Contractibility of Compressed Curves on 3-Manifold Boundaries
Erin Wolf Chambers, Francis Lazarus, Arnaud de Mesmay +1
In this paper we prove that the problem of deciding contractibility of an arbitrary closed curve on the boundary of a 3-manifold is in NP. We emphasize that the manifold and the cu…
cs.CG2019
Link Crossing Number is NP-hard
Arnaud de Mesmay, Marcus Schaefer, Eric Sedgwick
We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.