Regular Languages

Question

Which is the equivalent Regular Expression for the following: "Strings in which every group of 3 symbols should contain atleast 1 a."

a)[(a+b) (a+b)a]*

b) [(a+b) (a+b)a]* [(a+b)(a+b)a]*

c)[(ϵ + b + bb)a]* [ ϵ+ b + bb]

d) (abb)* (bab)b* (bba)*

Comments

@Ashish Lakhmani

$ \color{lightgray}{\Bigl  [ \bigl ( \color{black}{\varepsilon}  + b + bb \bigr )\; \color{black}{a} \;\Bigr ]^{\color{black}*} [ \color{black}{\varepsilon} + b + bb ]}$

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Thanks @Pragy Agarwal.

Is my approach right?

In option a, b, d there is possibility of strings which contain substring "bbb". That's why they are discarded.

So, answer is C.

 

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@Ashish Lakhmani Nopes, wrong approach. You can't generate bbb from option A or option B