Complexity of logarithmically alternating circuits with polylogarithmic cascading length
Determine the computational complexity of CCIRcasc,alt,size(O(log^t n), O(log n), n^{O(1)}) for any fixed t ∈ N^+, that is, logspace-uniform families of semi-unbounded fan-in cascading circuits of polynomial size, O(log n) alternations, and cascading length O((log n)^t).
References
For future research, we wish to list eight key open questions associated with aux-$k$-sna's and $k$-cascading circuits. In Section \ref{sec:P-connection}, the removal of the upper bounds of cascading length and alternations significantly increases the computational complexity of cascading circuits. If we expand only the cascading length from $k$ to $O(\logt{n})$, where $t$ is any constant in $N{+}$, then what is the computational complexity of $\mathrm{CCIRcasc,!alt,!size}(O(\logt{n}),O(\log{n}),n{O(1)})$?