P versus NC^1: explicit super-logarithmic depth lower bound

Establish the existence of an explicit Boolean function f: {0,1}^n -> {0,1} whose depth complexity under fan-in-2 AND/OR/NOT circuits (equivalently, De Morgan formulas) grows super-logarithmically with n, thereby separating P from NC^1.

Background

The paper studies depth lower bounds for Boolean formulas and circuits, with a focus on compositions and restricted top layers. Despite progress on restricted models, the central challenge remains proving super-logarithmic depth for an explicit function in the standard fan-in-2 model.

Achieving such a depth lower bound would resolve the P versus NC^1 problem. The authors note that the best known unconditional lower bounds are only (3−o(1))·log n, underscoring how far the field is from a complete resolution.