Which one of the regular expressions given below defines the same language as defined by the regular expression R?

(a (b a)^{*} + b (a b)^{*}) (a + b)^{+}

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(a (b a)^{*} + b (a b)^{*})^{*} (a + b)^{*}

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(a (b a)^{*} (a + b b) + b (a b)^{*} (b + a a)) (a + b)^{*}

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(a (b a)^{*} (a + b b) + b (a b)^{*} (b + a a)) (a + b)^{+}

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Solution

The correct option is C $(a (b a)^{} (a + b b) + b (a b)^{} (b + a a)) (a + b)^{}$
R = $(a + b)^{} (a a + b b) (a + b)^{}$ DFA corresponds to given regular expression R will be:

Which is equivalent to :

Which is equivalent to:

Which is equivalent to:

which is equivalent to

Hence equivalent regular expression is

$((b a)^{} (a + b b) + b (a b)^{} (b + a a)) (a + b)^{}$

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