One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de-Morgan formulas. Karchmer, Raz, and Wigderson suggested to approach this problem by proving that formula complexity behaves "as expected'' with respect to the composition of functions $f\circ g$. They showed that this conjecture, ... more >>>

One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}^1$). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested to approach this problem by proving that depth complexity behaves “as expected” with respect to the composition of functions $f ... more >>>

This is a purely pedagogical text.
We advocate using KW-games as a teaser (or ``riddle'') for a complexity theoretic course.
In particular, stating the KW-game for a familiar NP-complete problem such as 3-Colorability and asking to prove that it requires more than polylogarithmic communication poses a seemingly tractable question ... more >>>

One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq \mathbf{NC}^{1}$). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested to approach this problem by proving that depth complexity of a composition of functions $f \diamond g$ is roughly ... more >>>