  This paper exhibits a series of semantic characterisations of sublinear
nondeterministic complexity classes. These results fall into the general domain
of logic-based approaches to complexity theory and so-called implicit
computational complexity (ICC), i.e. descriptions of complexity classes without
reference to specific machine models. In particular, it relates strongly to ICC
results based on linear logic since the semantic framework considered stems
from work on the latter. Moreover, the obtained characterisations are of a
geometric nature: each class is characterised by a specific action of a group
by measure-preserving maps.
