There are a multitude of algorithms that can parse a context-free grammar in $O(n^3)$ time. Using matrix multiplication, one can even go asymptotically faster than that.
However, all algorithms for parsing arbitrary CFGs I know have a worst-case space usage of $\Omega(n^2)$ (although, admittedly, I have no idea what the space usage of that matrix multiplication algorithm is). I was wondering whether there are any algorithms that improve upon this space usage (so disregarding the time bound).
The question popped up into my mind after mentally linking $CSG = NDSPACE(n) \subseteq DSPACE(n^2)$ with the $\Omega(n^2)$ space bound on all the CFG parsing algorithms I knew. It's probably of no practical interest, but merely something I'd be interested in knowing.