Regular Expression

Question

$$\begin{align*} & \color{blue}{\text{Find regular expression for the following language}} \\ \\ &L = \left \{ xwx \; |\; x,w \in \left \{ a+b \right \}^{*} , |x| \leq 4 \right \} \\ \end{align*}$$

Answer 1

$|x| \le 4$, And w.r.to languages minimal value of $x = 0$(it cannot be negative)

So, We can consider any string to start and end with $\large \epsilon$. (considering $x = 0$)

So, RegExp would be : $\large \color{maroon}{(a+b)^*}$

For example : String $aa(abab)aa$, $\color{green}{x = aa,\; w = abab}$ can be mapped as $\color{green}{x = \epsilon, w = aaababaa}$

Comments

Put $w = ab$, and $x = \epsilon$

---

Yes, U r right

Thanks

---

i can also write ie as 

(a+b+epsilon)⁴(a+b)*(a+b+epsilon)⁴ 

can't this be true

Answer 2

when x is epsilon it will simply represent all the strings derivable, the set contains all strings derivable so the re will be (a+b)^*