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## Can I write a* + b* = (a + b)* ????

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NO  you cannot write
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To check equivalence of two regex create minimal DFA for both regex and if they are same then yes they are equivalent.
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sumit goyal 1 please explain the difference

+1
a* + b *  wil give { a , aa ,aaa ,aaaa ,......  , b,bb,bbb,bbbb,bbbb  , epsilon }

(a+b)* will give all possible combinations
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so how to create a DFA for this? a* + b *
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It is drawn like this

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sumit goyal 1 You forgot dead state.$4$ states will be there moreover first state is final

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i cretaed a nfa , so i didnot take dead state ,

NO,

we can write (a+b)*=(a*+b*)*

=(a*+b)*

=(a+b*)*

=(a*b*)*

=a*(ba*)*

=b*(ab*) *

or

make minimal dfa for both the RE and check LHS != RHS ,infact  language both are different

by Active (1.7k points)
edited by
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$(a+b)^* \neq (ab^*)^*$

And last one should be b*(ab*)*

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yes..by mistake correct one is

(a+b)*=(a*b*)*

=b*(ab*)*

=a*(ba*)*

+1 vote

$1^{st}$ one is RHS.
$2^{nd}$ one is LHS.
LHS $\neq$ RHS

by Active (1.3k points)
by Junior (951 points)

No ,because both are not same as u can see by the 1st REstring produce like ab,aabb.a,b,aa,bbetc but u can't get string like aba,aaabbabab,ababa etc .

whereas by the 2nt RE u will get all string produce by a and b.

by (173 points)