如何理解DFA（有限自动机）？

Question

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 string—a string with no letters in it—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?

Answer 1

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.

Answer 2

Good Evening ! yes after reading

 abcba 

you wil reach on (2) state..

double circle shows the Final State . ie shows acceptance of string the Destination

empty string or Lemda is accepted from a DFA it means that initial and final state is same for that DFA (language)