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?

  • 2
    $\begingroup$ Draw a picture of it, test it on some words. Then, if you are happy with it, prove that it is correct. $\endgroup$ Feb 5, 2015 at 20:34
  • $\begingroup$ You can use madebyevan.com/fsm to draw automata easily $\endgroup$
    – User
    Feb 5, 2015 at 21:02

1 Answer 1


Here is your suggested automaton, if I understand your transitions correctly (initial state is 1)

enter image description here

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).


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