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enter image description hereI have made two DFA’s for $ L= \{a^n b^n a | n\ge0\}$.

First one has several states. The second one is accepting an empty string also.

Somebody please guide me the correct one.

Zulfi.

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Since FSM's can't count identical sequences, I don't think both of your answers would be correct. You can take a look here, (pumping lemma) to prove why $L= \{a^nb^n | n \ge 0 \}$ is not regular, thus you can't write a FSM for it. Also a good example here shows the proof. On the other hand it would be different if you are meaning $a^*b^*a$ which can be written as a FSM.

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  • $\begingroup$ My question is : a^n b^n a, if we can draw a NFA i.e. also fine. $\endgroup$ Nov 30 '19 at 16:38
  • $\begingroup$ A NFA is also a FSM, so you I'm pretty sure you can't draw one $\endgroup$ Nov 30 '19 at 17:43
  • $\begingroup$ But you said that "On the other hand it would be different if you are meaning a∗b∗a which can be written as a FSM." $\endgroup$ Nov 30 '19 at 19:32
  • $\begingroup$ Yeah but $a^*b^*a$ is different than $a^nb^na$. If you want the first one it's easy we can write it. $\endgroup$ Dec 1 '19 at 1:41
  • $\begingroup$ Yes its a^*b^*a. I think we don't have a counting problem in this case because number of a's and b's are not equal. $\endgroup$ Dec 1 '19 at 3:05

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