Space complexity of Chomsky Normal Form
It is well-known, and stated in Wikipedia (which gives a reference: Lange and Leiß), that there is an algorithm transforming an arbitrary context-free grammar $G$ into a grammar in Chomsky normal form of size $O(|G|^2)$.

The following grammar might be an example showing that the quadratic blow-up is necessary:
$$
\begin{align*}
&amp;S \to A_1 \ldots A_m \\
&amp;A_1 \to A_2 \mid \sigma_1 \\
&amp;A_2 \to A_3 \mid \sigma_2 \\
&amp;\cdots \\
&amp;A_{m-1} \to A_m \mid \sigma_{m-1} \\
&amp;A_m \to \sigma_m
\end{align*}
$$
This grammar has size $\Theta(m)$, and it seems that every grammar in Chomsky normal form for this language must have size $\Omega(m^2)$.