Accepting state
Also known as: Final state, Accept state
An accepting state (final state) is a state in $F$ where an accepter says yes if the input ends there.
For a DFA, run $\delta^$ from the start; accept iff the unique end state is in $F$. For an NFA, accept iff *some run ends in $F$. Diagrams usually mark finals with a double circle.
The language of the machine is exactly the strings whose runs finish accepting. No $F$ means transducers or pure controllers: output matters, not membership.