We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a new perspective. We present a framework for understanding Circuit Complexity through the lens of Information Theory with analogies to results in Kolmogorov Complexity, viewing circuits as descriptions of truth tables, encoded in logical gates and wires, rather than purely computational devices. From this framework, we re-prove some existing strong Circuit Complexity bounds, explain what the optimal circuits for most Boolean functions look like structurally, give insight into new circuit bounds, and explain the aforementioned results in a unifying intuition that re-frames time entirely.

翻译：我们从新视角重新审视电路复杂性的基本原理与高效计算的本质。本文提出一个通过信息论视角理解电路复杂性的框架，类比柯尔莫哥洛夫复杂性的结果，将电路视为真值表的描述（编码于逻辑门与连线中），而非纯粹的计算设备。基于此框架，我们重新证明了一些已有的强电路复杂性下界，解释了大多数布尔函数的最优电路在结构上的特征，为新的电路下界提供了洞见，并以一种将时间概念完全重构的统一直观方式阐释了上述结果。