Explicit Boolean function with quadratic DRE complexity

Identify an explicit Boolean function with decomposable randomized encoding complexity Ω(n²), thereby replacing the paper’s nonconstructive existential quadratic lower bound with a constructive example.

Background

The paper’s Ω(n²) lower bound for general Boolean functions is obtained by a counting argument and is therefore nonconstructive. Earlier work gives explicit examples, such as Element Distinctness and Clique, with Ω(n²/log n) lower bounds, but the paper does not provide an explicit function achieving a genuinely quadratic bound.

The authors also mention that a candidate pseudorandom function has a quadratic-size DRE under a security assumption, creating a natural-proofs barrier to constructive superquadratic lower bounds.