[Doubt] Conversion of finite automata to regular expression

Question

How to convert given finite state automaton into regular expression.

Comments

@joshi_nistish, Earlier I made a mistake while making FSA. I made correction and updated the question. Can you please write regular expression again for above diagram? and Can you also check whether I made correct FSA for this grammar or not:
                S        →        y | z | y S | z S | x B
                B       →        y | y S
Thank you.

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RE:-

(xy+y+z)* (xy+y+z) / (xy+y+z)⁺  

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@hs_yadav Can you please explain how did you get the answer?

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 @tonystark007

by using state elimination method:-

1.eliminate all intermediate state but no transition should be lost...

and in your grammar for RE is:-

 S        →        y | z | y S | z S | x B 
 B       →        y | y S

correct....

here you have taken as...

1.any no. y or any no. of z (at least one y or z) but every x should be followed by y. means (z⁺+y⁺+(xy)⁺)⁺

you can also do like this...

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@hs_yadav I tried to solve this with state elimination method. But I confused how to remove q1 state as Y is going back to q0 state.

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when you will remove q1, then loop 'xy' will be added on q0 as well as transition 'xy' will be added from q0->q2

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let we have removed q1 then what is the all transitions which may be lost....

1. q0->q1->q0     xy    (it could be represented as self loop on q0)

2.q0->q1->q2      xy    (it could be obtained by taking transition from qo->q2 as xy)

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I didn't knew how to handle this case. Thank you very much :)

Answer 1

"  (X+Y)*X (Y(X+Y)X)* (X+Y) (Y+Z)   "  i got this RE

Answer 2

(yz+(x+z))*(y+y+z)

Comments

Plz explain it with state elimination method