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：我们从新的视角重新审视电路复杂性的基本原理与高效计算的本质。我们提出一个框架，通过信息论的视角来理解电路复杂性，并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（编码于逻辑门与导线中），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最优电路的结构特征，为新的电路下界提供了洞见，并以一种统一且彻底重构时间概念的直观方式阐释了上述结果。