Computation and Regular Expressions - Find a regular expression for the following scenarios

Question

Find regular expressions for:

• A. All binary strings with exactly two $1’s$

• B. The set $\{a^nb^m :n\geq3, m$ is even$\}$

• C. All binary strings with a double symbol (contains $00$ or $11$) somewhere.

• D. The language on $\Sigma=\{a,b\}, L=\{w:n_a(w) \mod 3=0\}$

Answer 1

$1.L_{1}=0^{*}10^{*}10^{*}$

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$2.L_{2}=aaaa^{*}\left ( bb \right )^{*}$

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$3.L_{3}=\left ( 0+1 \right )^{*}00\left ( 0+1 \right )^{*}+\left ( 0+1 \right )^{*}11\left ( 0+1 \right )^{*}$

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$4.L_{4}=b^{*}(ab^{*}ab^{*}ab^{*})^{*}$

Comments

for L4 why not   b*(ab*ab*ab*)*   ?

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@diksha , yes you are correct.Thanks

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L4 can also be expressed as (b + ab*ab*a)*

Answer 2

solution

Ans1.   0*10*10*

Answer 3

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