Finite automata to regular expression conversion in theory of automata

By: Prof. Fazal Rehman Shamil | Whatsapp:+923028700085

How we convert the following Finite Automata into Regular expression?

Let’s start drawing the FSA.

FSA in theory of computation

we can see that we can move left or we can move right from start state, so we need to build two R.E and then to combine them.

Left part of FA:

Step State R.E
1 start b
2 3 b*
3 3 a
4 end5 a*
5 end5 Moving back by loop
Now, add all the R.E from step 1 to 4 and loop it again and again by step 5.

R.E = step1 + step2+ step3+ step4.

R.E = b b* a a* 

For moving back for getting more and more string we can have kleen star closure as mentioned in step 5.

So, 

R.E = (step1 + step2+ step3+ step4)*

R.E = ( b b* a a*  )*

The right part of FA

Step State R.E
1 start a
2 2 a*
3 2 b
4 end4 b*
5 end4 Moving back by loop
Now, add all the R.E from step 1 to 4 and loop it again and again by step 5.

R.E = step1 + step2+ step3+ step4

R.E = a a* b b*

For moving back for getting more and more string we can have kleen star closure as mentioned in step 5.

So, 

R.E = (step1 + step2+ step3+ step4)*

R.E = ( a a* b b* )*

 

Now we combine the left and right R.E by having an option. So the final R.E will be as follows.

R.E = Left part of R.E OR Right part of R.E

R.E = ( b b* a a*  )*  +   ( a a* b b* )*

Video Lecture

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