We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a fresh 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 Circuit Complexity bounds, explain what the optimal circuits for most boolean functions look like structurally, give an explicit boolean function family that requires exponential circuits, and explain the aforementioned results in a unifying intuition that re-frames time entirely.

翻译：我们从一个全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。本文提出一个通过信息论视角理解电路复杂性的框架，该框架与柯尔莫哥洛夫复杂性的结果形成类比，将电路视为真值表的描述（编码于逻辑门与连线中），而非纯粹的计算装置。基于此框架，我们重新证明了若干已有的电路复杂性下界，解释了大多数布尔函数的最优电路在结构上的特征，给出了一个需要指数级电路的显式布尔函数族，并将上述结果置于一个统一的理论框架中加以阐释，该框架从根本上重构了对时间的理解。