  We introduce a notion of contextuality for transformations in sequential
contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of
contextuality. Within a transformation-based model for quantum computation we
show that strong sequential-transformation contextuality is necessary and
sufficient for deterministic computation of non-linear functions if classical
components are restricted to mod2-linearity and matching constraints apply to
any underlying ontology. For probabilistic computation,
sequential-transformation contextuality is necessary and sufficient for
advantage in this task and the degree of advantage quantifiably relates to the
degree of contextuality.
