Finite state Machine

Question

which of the following statement is True?

a) r* and  r+ are always different.          b) r* and r+ may be equal.

 

Please explain briefly.

Comments

Take r= epsilon

Answer 1

According to me  option A is true

Comments

 ε*= ε

It is not equal to Φ .

Please read the identities of regular expressions

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yes, u r right.

if r=ϵ,then r*={ϵ} and r+={ϵ}.

so ,Options b is True .

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yup i was wrong its actually  Φ*=ϵ thanks for correcting

Answer 2

a) r* and  r+ are always different.          b) r* and r+ may be equal.
if r= epsilon

epsilon* = epsilon

epsilon+ = epsilon

from above b is correct

 but if u place

r= phi

phi*= epsilon

phi+ = phi

which is different so it is corrected as fore some condition r+ and r* are smae and for some they are different

Comments

both are correct?

Answer 3

r* means *>= 0,

i.e. r* = {Ɛ,r,rr,rrr,rrrr.....}

but in the case of r+,

r can not be equal to 0 i.e. in simple words + denotes that language contains atleast one r.

i.e. r+ = {r,rr,rrr,rrrr.....}

Hence r* and r+ are always different.