Making a finite automata How can I make a finite automaton which does not end in string ab.

With the alphabet a,b

I made 3 states. For the first one it is accepting states and thus accept the empty string.

So here is a table I made. State 1 is initial state

        input   goes to state input goes to state


State 1  

         b       1             a      2


state 2

          b       3             a       2


state 3   

            b       3              a      3


But will it work?
Here is your suggested automaton, if I understand your transitions correctly (initial state is 1)



This automaton will only accept $\epsilon$, and words consisting of a number of $b$'s

Hints to make one that accepts your language:

Make sure that it accepts $\epsilon, a, b$ and make sure that you "move away" from accepting states when seeing a $b$ after an $a$ (keep in mind that $aabb$ is also a string in the language, i.e the second $b$ should make the machine go to an accepting state).