I have an encoding of an unambiguous grammar $G$. Can I apply a morphism $σ$ so that the grammar becomes ambiguous?
I have no clear concepts about this, only the idea: "grammar $G$ is ambiguous if there's a string $x \in L(G)$ having two different leftmost derivations in $G$". I would like a good explanation and if it's possible, an example.
I will consider two alphabets, $Σ_1$ and $Σ_2$, where $\Sigma_1$ is the terminal alphabet of $G$. A morphism is a function of the form $h\colon Σ_1^* \to Σ_2^*$ which satisfies: $h(xy)=h(x)h(y)$ for all $x,y \in \Sigma_1^*$. When applying the morphism to a grammar on $\Sigma_1$, the result is a grammar on $\Sigma_2$ (that is, the morphism is only applied to the terminals in $G$).