02 February 2018 0 2K Report

A known theorem staes that if $f$ is a function from $\left\{0,1\right\}^{n}$ to $\{0,1\right\}$ that has a critical input, cannot be computed by any CREW PRAM machine (i.e. regardless of the number of processors) in less than $\log_{2}\left(n\right)$.

A function as above has a critical input if there exist $I\in\left\{0,1\right\}^{n}$ such that $f\left(I\right)\not = f\left(I_{j}\right)$ for any $j$, where $I_{j}$ is $I$ cahged in a single bit in the $j$'th place.

I will be happy if one can advise some refference regarding a simple proof of this theorem.

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