How do we determine minimum $k$ such that $G$ is a strong $LL(k)$ Grammar
Like for grammar $G$ with the following rules $S\rightarrow aAcaa \mid bAbcc,A\rightarrow a \mid ab \mid \epsilon$
I do not believe one can obtain directly a minimum $k$ such that $G$ is a strong $LL(k)$ grammar. However, as it is possible to (dis)prove that a grammar is strong $LL(k)$, one can iterate the proof over $k$.
A grammar $G$ is strong $LL(k)$ iff for every pair of distinct production rules $A \to \alpha$ and $A \to \beta$ (with $\alpha \neq \beta$), we have:
$$ First_k( \alpha \; Follow_k(A) ) \; \cap \; First_k( \beta \; Follow_k(A) ) = \emptyset $$
The steps to obtain a $k$ for a certain grammar $G$ are thus as follows:
Some documents that might help with the actual proof: