Regular Expression || Linz 3.2

Question

Regular Expression for this FA ?

Comments

I found $\begin{align*} a^{*}b\left ( aa \right )^{*}\left ( \epsilon + a \right ) \end{align*}$. please verify.

Answer 1

In the given FA , both the final states are equivalent ..So we can remove one of them 

and can write the regular expression as :  a*b ( ϵ + a.a* ) ..

Now we know for a regular expression r , we can write :  ϵ + r . r*  = r* 

So here the regular expression is simplified as : a* b a*

Comments

here also $\begin{align*} a^{*}b\left ( aa \right )^{*}\left ( \epsilon + a \right ) \end{align*}$ ..last part can easily be removed and replaed as $a^{*}$. Thanks for the observation !

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Good approach :)

Answer 2

$If \:R=Q+RP \:then \:R=QP^*\\ q_{1} = q_1a + \epsilon \\ q_{2} = q_1b+q_3a\\ q_3=q_1b+q_2a \\ q_1 = a^{*} \\ Now \: q_2 = a^*b+q_3a \\ Subtitute\: q_2 \:in \:q_3 \\ q_3=a^*b+(a^*b+q_3a)a \\ q_3=a^*b+a^*ba+q_3aa \\ q_3 =(a^*b+a^*ba)(aa)^*$

Comments

Arden..nice !! but in your case answer should be $q_2+q_3$. right ? Although $q_2$ may a subset of $q_3$, you have not shown