Are all final states reachable from the starting states of a DFA?

Question

Suppose that DFA D is a valid DFA. What would this imply regarding the reachability of its final states from initial states? May I assume this:

$\delta^* (q_0, w) = f$, where $w \in \Sigma$ and $f \in F$

Answer 1

No, you cannot assume this. It's perfectly consistent with the definition of a DFA for there to be states which are unreachable from the starting state. What you can do is start with a DFA and filter it down to just the states reachable from the start state without changing the language of the DFA, though, if you think it would help.

Hope this helps!