I am working a bit with a book from Sipser (Introduction to the theory of computation, 3rd Ed.).
On page 187 in exercise 3.4 one is asked to give a "..formal definition of an enumerator.[..]"
Is the following ok/correct?
Let $A$ be a recursive enumerable language over alphabet $\Sigma$.
(That would be, as I understood, $A \subset \Sigma^*$, and there is a TM $M_A$ such that for all $a \in \Sigma^*$:
$a\in A $ if and only if $M_A$ accepts $a$.)
Let $E_A$ be a TM with 2 tapes. Then:
We call $E_A$ an enumerator of the language $A$ if and only if
for all $a \in \Sigma^*$: ($a \in A$ if and only if $a$ will eventually appear on the second tape.)
Thank you