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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?

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    $\begingroup$ Draw a picture of it, test it on some words. Then, if you are happy with it, prove that it is correct. $\endgroup$ – Dave Clarke Feb 5 '15 at 20:34
  • $\begingroup$ You can use madebyevan.com/fsm to draw automata easily $\endgroup$ – User Feb 5 '15 at 21:02
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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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