Doubt regarding closures

Question

Are (bx)* b and b(xb)* equivalent?

Comments

yes they are deriving the same sets

Answer 1

Deriving same strings try writing string set for both language. It will be same

Answer 2

No .

Because (bx)*b are deriving all strings ending with b

And b(xb)* are deriving all strings starting with b.

Moreover first one can derive the string "bbxxb" whereas second one cannot derive this string.

Hence, they are not equivalent.

Comments

you have taken wrong example bbxxb can not derive from any of set
Even both are equivalent since both are generating string that start and ends with b.

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Why (bx)*b cannot derive "bbxxb"?

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@nandini Gupta.I assume you have considered both expressions as one while they are not a common expression.  (bx)*b means any number of bx first then b. But bx in pair not xb and bx. here it's not b*x* it's (bx)* repeation will be in pairr only.

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@nandini

 

None on the expressions can derive bbxxb

The only string they can derive is bxbxbxbxb....

Answer 3

Yes they are same by shifting property.

Answer 4

Both Regelar expressions are equivalent

The language derived is a bxbxbxbxb......

In 1st case u r focusing on the 1st 'b'  recursing the rest

Where as in 2nd case u are focusing on last 'b'  recursing what's ahead of it

But ultimately both derive the same language

This is a good example to show that regular expression being non deterministic in nature can have more than 1 regular expressions for the same language

Answer 5

yup it is equivalent