# Regular expression for a finite automaton appears to be wrong

For the following finite state machine:

The language recognized by it is given to be: $0+(10+11)(0+1)^*$ in my samples book, which I think is clearly wrong, since there's no return path to the final state.

I think the language recognized should be just an epsilon or nothing. I wanted to confirm if I am right or wrong with the answer.

• You may only consider there is a typo in your book and that the final state should be $C$. But then the language recognized by the automaton should be $(0+(10+11))(0+1)^*$. – J.-E. Pin Apr 3 '16 at 13:58
• You have already pretty much proven that that solution is wrong. What more do you need? – Raphael Apr 3 '16 at 14:04
• Considering your analysis of the automaton with the typo: "...an epsilon or nothing". If a finite automaton represents the empty language then all its accepting states must be unreachable from the start state, and this is clearly not the case here. – Anton Trunov Apr 3 '16 at 14:22
• As JEP shows, the book contains two typos. What book does not? :-) – phs Apr 4 '16 at 11:25

As given FA is DFA. It is accepting string only $\{\epsilon \}$.
And, complement of given DFA accepting : $\implies (1+0+1(0+1))(0+1)^*= (1+0+(10+11))(0+1)^*$
$\implies 1(0+1)^*+0(0+1)^*+(10+11)(0+1)^* = (0+1)^+ =$ { accepting everything other than $\{\epsilon \}$ string over alphabet $\{0,1\}$}.