Extend Meir’s strong composition theorem to standard composition

Establish an analogue of Meir’s strong composition theorem for the standard block composition f ◇ g of Boolean functions, rather than for the strong composition variant.

Background

Meir’s strong composition theorem provides a significant partial result toward KRW-type lower bounds but for a stronger notion of composition. Bridging the gap between strong and standard composition is essential for applying these techniques to the usual block composition model.

The authors note that despite this progress, an analogous theorem for standard composition is not known.