# DFA (Finite Automata), please help me to understand

Indicate the state that the DFA will end in after processing each of the following input strings. Note: the input labeled "The empty string" is literally the empty stringâ€”a string with no letters in itâ€”not the letters 'T', 'h', 'e', ' ', 'e', and so forth.

For the string = abcba,

do I end in state 2? Also, what is that double circle means?

### 2 Answers

From https://www.tutorialspoint.com/automata_theory/deterministic_finite_automaton.htm

The vertices represent the states.
The arcs labeled with an input alphabet show the transitions.
The initial state is denoted by an empty single incoming arc.
**The final state is indicated by double circles.**

And I'm not really sure but I think you stop at 2.

cheers

Yes, after abcba, you end in state 2.

The double-circle usually indicates an accepting state -- in the DFA for a regular expression, the string you've received so far matches the regular expression iff you're in an accepting state.

If a regular expression matches the empty string then the start state will also be an accepting state, as is the case here.