  We study reliable communication over point-to-point adversarial channels in
which the adversary can observe the transmitted codeword via some function that
takes the $n$-bit codeword as input and computes an $rn$-bit output for some
given $r \in [0,1]$. We consider the scenario where the $rn$-bit observation is
computationally bounded -- the adversary is free to choose an arbitrary
observation function as long as the function can be computed using a polynomial
amount of computational resources. This observation-based restriction differs
from conventional channel-based computational limitations, where in the later
case, the resource limitation applies to the computation of the (adversarial)
channel error. For all $r \in [0,1-H(p)]$ where $H(\cdot)$ is the binary
entropy function and $p$ is the adversary's error budget, we characterize the
capacity of the above channel. For this range of $r$, we find that the capacity
is identical to the completely obvious setting ($r=0$). This result can be
viewed as a generalization of known results on myopic adversaries and channels
with active eavesdroppers for which the observation process depends on a fixed
distribution and fixed-linear structure, respectively, that cannot be chosen
arbitrarily by the adversary.
