Theory Of Computation

Question

Hi.  please tell me the Regular Expresion of image given DFA below

Comments

Sir the answere given is but oi am not able to understand it so can you please explain also

[1+01+00(0+10)^* 11]^* 00(0+10)^*
Explanation:
1] Add a final state to the given FA,

2] Eliminate q₂, we get the following

3] Eliminate q₃, we get the following
This gives us the following regular expression for the language of our FA,
(1+01+00(0+10)* 11)* 00(0+10)*

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what is the problem in this explanation?everything is explained.

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Sir what about your expression which  you have mentioned

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that was wrong.I checked again and I found a mistake.

Answer 1

1*0(10)*0(0+10)*

Explanation :

By looking at the DFA one can easily tell, the DFA accepts the set of strings that ends in two consecutive zeroes or ends in "10".

In state 1 : If we get 1's, we loop over. Hence 1*

In state 2 : We reach here by scanning single zero. If we scan a 1, our pattern is destroyed and hence we should can two zeros again hence going to state 1 again. So used (10)*

State 3 : if we scan another zero on state 1, we move to final state 2, because our pattern is complete now and we can scan any number of zeroes and stay at final state.

If a 1 occurs at final state, our pattern is destroyed but we can also scan a 10, hence the last state can scan either a 0 or 10 to stay in final state so used. (0 + 10)*

So the RE is : 1*0(10)*0(0+10)*