I have an encoding of an unambiguous grammar $G$. Can I apply a morphism $$ 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.Morphism:I will consider two alphabets,  $_1$ and $_2$, where $\Sigma_1$ is the terminal alphabet of $G$.A morphism is a function of the form $h\colon _1^* \to _2^*$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 $G$).
Making a grammar ambiguous by applying a morphism
formal languages;formal grammars;ambiguity
The answer depends on the grammar $G$. If $G$ generates at most one word, then no morphism will make it ambiguous (prove!). If $G$ generates more than one word, then the morphism sending all characters to the empty string will make it ambiguous (why?).