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.

翻译：我们研究点对点对点对点对面的对立渠道的可靠通信,对手可以通过这种功能观察传送的代码词,这种功能可以将美元比位编码作为输入,并对某些给定美元[0,1,1]美元计算出美元比值输出。我们考虑美元比值观测是计算结合的情景 -- 敌国可以自由选择任意观察功能,只要该功能可以用计算资源的多元数量来计算。这种基于观察的限制不同于常规的基于频道的计算限制,在后一种情况下,资源限制适用于计算(对抗性)频道错误。对于所有美元比值[0,1-H(p)],美元是二进方英英英英美函数,美元是敌人错误预算,我们确定上述频道的能力。关于美元的范围,我们发现这种能力与基于频道的常规计算限制是相同的,在后一种情况下,资源限制适用于计算(对抗性)频道错误的计算结果。对于所有美元,[0,1-H(cdoit)美元是美元,而美元是双英美的双英美计算结果,通过一个固定的直径结构来决定固定的直观分布。