  We discuss the interdependence of resource state, measurement setting and
temporal order in measurement-based quantum computation. The possible temporal
orders of measurement events are constrained by the principle that the
randomness inherent in quantum measurement should not affect the outcome of the
computation. We provide a classification for all temporal relations among
measurement events compatible with a given initial stabilizer state and
measurement setting, in terms of a matroid. Conversely, we show that classical
processing relations necessary for turning the local measurement outcomes into
computational output determine the resource state and measurement setting up to
local equivalence. Further, we find a symmetry transformation related to local
complementation that leaves the temporal relations invariant.
