Consider the membership problem for a context-free language. An instance of this problem can be described as pair $(G,w)$, where $G$ is a context-free grammar and $w$ is a string.
Lets say I have a PRAM and I want it to decide in $\log^k n$ time and $n^c$ space complexity whether $w$ is in $L(G)$ ($c$ and $k$ are both constants) – that is, the complexity stays within Nick's class.
Is there such an algorithm? If so what would be an idea?