i think this must be re

2 votes

Regular Expression for the following Language,

$$\begin{align*} L = \left \{ a^{m}b^{n}\; | m \geq 1,n \geq 1,mn \geq 3 \right \} \end{align*}$$

$$\begin{align*} L = \left \{ a^{m}b^{n}\; | m \geq 1,n \geq 1,mn \geq 3 \right \} \end{align*}$$

8 votes

Best answer

Minimal strings of above language are : $\color{green}{aaab, aabb}$ and $\color{green}{abbb}$ as minimal value of $m$ and $n$ is $1$, and also $mn \ge 3$.

Minimal pairs of $m$ and $n$ that satisfy above constraints are: $(m,n) = (1,3), (3,1)$ and $(2,2)$

So, RegExp would be : $\color{maroon}{aa^*bbbb^* + aaaa^*bb^* + aaa^*bbb^*}$

Minimal pairs of $m$ and $n$ that satisfy above constraints are: $(m,n) = (1,3), (3,1)$ and $(2,2)$

So, RegExp would be : $\color{maroon}{aa^*bbbb^* + aaaa^*bb^* + aaa^*bbb^*}$

2

Along with the GATE syllabus, do we need to by heart this " \color{green}{text to be coloured} between $$." :)

Or any shortcut button on the LATeX.

Or any shortcut button on the LATeX.