Finite automaton issue: the proposed solution has a fourth state, whereas I found only 3.

Question

The task is:

Construct a determistic finite automaton M, with a maximum of four states, that recognizes all binary strings that starts with a 0, and has an odd number of 1's.

I've included a image of my answer, and the correct solution. What am I doing wrong? Why does the solution include the state $s_3$? Is it because it's a determistic automaton, and without it I don't account for all possible strings?

The machines in question

Thanks for the help.

Answer 1

You have have something for the machine to do in case it encounters a $1$ at the start of the string. Your machine doesn't work then, while the solution goes into an eternal loop in state $S_3$.