Bridson–Wilton virtual specialness undecidability conjecture

Let $Y$ be a finite nonpositively curved square complex. A square complex is virtually special if it has a finite-sheeted cover that is special. Bridson–Wilton's conjecture. There does not exist an algorithm that, given $Y$, determines whether or not $Y$ is virtually special. The source relates this conjecture to a question about $VH$-complexes and tilings, but gives no resolution.