I want to verify if I am correct in my interpretation of the $\mathrm{NC}^i$ model.
In this model the input is given to at most $O(n^k)$ processors and each processor takes at most $O(\log^i n)$ time to arrive at a solution.
Can the processors communicate on any intermediate data?
How is the result whether accept or reject announced?
A fine grained problem
So the output of the algorithm can depend on partial results computed on previous processors?
There are $O(n^k)$ processors. So even if each processor computes $1$ bit of intermediate data that is useful for all processors then reading the intermediate results will itself take $\Omega(n^k)$ time then there is no way processors can finish in $O(\log^in)$ time.
So what limitations are there in the length and dependency on intermediate results?