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

in Theory of Computation by Active (3.9k points)
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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 ,

4 Answers

+2 votes

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
0

$(a+b)^* \neq (ab^*)^*$

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)
0 votes
by Junior (951 points)
0 votes

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)
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