I have a problem with this following question:Prove that the language $\{uw : |u|=2|w|\}$ is regular. I tried to give this regular expression $(uw)^*$ to resolve it.
Prove that the language { uw : |u| =2 |w| } is regular
formal languages;regular languages;regular expressions
Any string of the form $uw$ where $|u| = 2|w|$ is a string whose length is a multiple of $3$. We are therefore considering the language of strings over some alphabet $\Sigma = \{ a_1, \ldots, a_k \}$ (not specified in the question). whose length is a multiple of $3$. Let $\Sigma$ be the regular expression $a_1 + \cdots + a_k$. Then a regular expression descring the language in question is$$(\Sigma\Sigma\Sigma)^*$$