# The reverse DFA is not working as expected

Assume a regular language contains all the strings that are ended with "01". We can draw the following DFA for it:

And I reversed the DFA according to this answer (designing a DFA and the reverse of it)

I expected this DFA to accept all strings that start with "10" but it is not. What is my mistake in drawing the reverse DFA?

• Can you give a counter example? Nov 3 '18 at 21:58
• The reverse "DFA" is a finite state automaton, but it is not deterministic. It does accept every string that starts with $10$ but you will have to select the proper path. So for example, for the string $100$ you do not follow the path from left to right (as you might expect) because you will get stuck. Instead you take the loop with $0$ in the middle state. Nov 4 '18 at 1:17
• @HendrikJan You are right. The machine accepts all the string starting with "10"; you should just follow the correct path. Nov 4 '18 at 16:32