Accordingly, to the question Chomsky Hierarchy and P vs NP, Context-Sensitive Grammars are on Linear Space.
Assuming a Deterministic Parser is the one which can parse unambiguous grammars in something like linear time complexity, while a NonDeterministic Parser can parse any grammar in some worst time complexity like $O(n^5)$ or exponential.
- When something is on Linear Space, it takes Exponential time to be parsed by a Deterministic Parser? (probably space complexity has no relation to its time complexity, maybe something in $NSPACE(n)$ or $PSPACE(n^2)$ can affect time complexity?)
- Can any Context Sensitive Grammar be parsed in a Polynomial Complexity Time?