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Could someone provide an explanation of how to convert this DFA into a regular expression? I have found three methods online, ie: How to convert finite automata to regular expressions?

but they are all very confusing to me.

The automaton is:

$$M = ((1,2,3), 1, \{a,b\}, \delta, \{1,3\})$$ where

$$\delta(1,a) = 2\\ \delta(1,b) = 2\\ \delta(2,a) = 2\\ \delta(2,b) = 3\\ \delta(3,b) = 2\\ \delta(3,a) = 1$$

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chibro2
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    What part is causing the confusion? I also suggest starting with the state removal method, it's simple and visual (but easy to miss things in larger automata). – Luke Mathieson Jan 28 '15 at 03:55
  • wrt to the state removal method, I am not sure how to assign the arrows after removing some state. – chibro2 Jan 28 '15 at 04:12
  • Given a state to remove $w$, you look at every ordered pair $u$, $v$ of remaining states, and see if there was a set of transitions $u\rightarrow w$ labelled with $r_{1}$, $w \rightarrow w$ labelled with $r_{2}$ and $w \rightarrow v$ labelled with $r_{3}$, if there is, then after removing $w$, add a transtion $u\rightarrow v$ labelled with $r_{1}r_{2}^{\ast}r_{3}$. – Luke Mathieson Jan 28 '15 at 10:52
  • The reference question you found contains examples for all methods. It is not clear what your problem is, and how it can be solved without reproducing content from the reference question here (needlessly). (I don't consider just solving the exercise for you likely to be of help.) – Raphael Jan 28 '15 at 11:01

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