  In this paper, we first present an outer bound for a general interference
channel with a cognitive relay, i.e., a relay that has non-causal knowledge of
both independent messages transmitted in the interference channel. This outer
bound reduces to the capacity region of the deterministic broadcast channel and
of the deterministic cognitive interference channel through nulling of certain
channel inputs. It does not, however, reduce to that of certain deterministic
interference channels for which capacity is known. As such, we subsequently
tighten the bound for channels whose outputs satisfy an "invertibility"
condition. This second outer bound now reduces to the capacity of this special
class of deterministic interference channels. The second outer bound is further
tightened for the high SNR deterministic approximation of the Gaussian
interference channel with a cognitive relay by exploiting the special structure
of the interference. We provide an example that suggests that this third bound
is tight in at least some parameter regimes for the high SNR deterministic
approximation of the Gaussian channel. Another example shows that the third
bound is capacity in the special case where there are no direct links between
the non-cognitive transmitters.
