One of the major open problems in complexity theory is proving super-polynomial lower bounds for circuits with logarithmic depth (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}_1~$). This problem is interesting for two reasons: first, it is tightly related to understanding the power of parallel computation and of small-space computation; second, it is one of the ... 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 >>>