Show that if a language L over the alphabet Σ is accepted by a deterministic PDA, then the language {u#v | u €L and uv €L} for some symbol # NOT contained in Σ is accepted by PDA. A qualitative convincing argument is all that is required.

Question

anonymous · Answer

Since the new language has a symbol that isn't in $\Sigma$, I find it a bit weird that we know it will accept the symbol $\#$.

anonymous · Answer

I mean  hypothetically, suppose $L$ is just empty strings.  Our new language accepts $\#$, which is not an empty string.  Therefore a PDA accepting only empty strings would accept $L$ but not our new language.

So I must be misreading somehow.