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Consider this regular expression:  r = (a*b)* + (b*a)*

This is equivalent to

(a) (a + b)*

(b) (a + b)* · (ab)+ + (a + b)* (ba)+

(c) (a + b)*a + (a + b)* b

(d) None of above

edited | 116 views
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a should be answer ...as eplison is generated by r and a ..and other strings too ..
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but how aaba string is generated from  r
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from (b* a)* ===> take 3 times

1) a by taking b* = ∈

2) a by taking b* = ∈

3) ba by taking b* = b
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tq
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i think option (d) is correct .ababa is not in the language but can be generated by option (a) so none of these is coorect option.
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hi .. look at this :

in option B) just consider second part ...that is   (a + b)* (ba)+

now (a+b)^3(ba)+ gives us =(a+b)(a+b)(a+b)(ba) now i have option that from first 3 brackest i can take a or b as per my wish ..so

take a form 1st b from second and a agian from 3rd so we get (ababa)...so string generated, similarily you can take First part of C option and cross check that same string can also be genertaed by option C.

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is ababa is in original language??????can you generate it  from original language???
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Yes you can generate ababa from given language
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how?????
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take second part of r

that is ((b*a)*

now take b* as episolon = (b^0 .a)(b^1a)(b^1a)...generated form it.

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oh its my mistake.but option(a) is not correct.
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a is correct bro ...it generates strings with alpahabets a and b with Epsilon too ..

while b and c also generate same except that they failed to generate epsilon.