How to mark things in the input? Sipser theorem 4.4*
$E_{DFA} = \{ \langle A \rangle \mid \text{A is a DFA and } L(A)=\emptyset\}$ is decidable.

I could not quite understand the solution, I'll quote it:

On input $\langle A \rangle$ where $A$ is a DFA:

Mark the start state of A

Repeat until no new states get marked:

Mark any state that has a transition coming into it from any state that is already marked.

If no accept state is marked, accept; otherwise, reject.



My question is, what does it mean to even 'mark' something in the encoding? how do we do this? The encoding is merely a word from $\{A,c\}$, how would you 'mark' states?
It's just a colloquialism.  It means, you keep a set of states that have been marked.  Initially the set is empty.  When you mark a state, you add it to that set.