# Is there a DFA that accepts no string, but has at least one final state?

Is there a DFA that accepts no string, but has at least one final state?

I think it would be possible to make a DFA that accepts no string only by creating no final states or by making sure that the final states are not accessible. But how can a state not be accessible if a DFA has all of its transitions defined?

• It is certainly possible, and I challenge you to find an example. Be creative. Feb 4 '17 at 22:40
• cs.stackexchange.com/q/65180/755
– D.W.
Feb 10 '17 at 5:47

Consider a 2-state DFA over the alphabet $\{a\}$ (single character alphabet) that accepts only the empty string:
In this DFA, state 0 is the start state, and also the only accepting state. Now, if state 1 were the start state (but state 0 still the only accepting state), what strings would this machine accept?