  We address the question of whether the property of being virtually special
(in the sense of Haglund and Wise) is algorithmically decidable for finite,
non-positively curved cube complexes. Our main theorem shows that it cannot be
decided locally, i.e. by examining one hyperplane at a time. Specifically, we
prove that there does not exist an algorithm that, given a compact
non-positively squared 2-complex X and a hyperplane H in X can decide whether
or not there is a finite-sheeted cover of X in which no lift of H
self-osculates.
