# What does ({a,b}*)² mean?

Pretty much just the title. Is it all possible combinations of a and b that have 2 letters ?

• Probably means $\{a,b\}^*\cdot \{a,b\}^*$ where $\cdot$ is the concatenation operation for languages. In this case, its not hard to show that $(\{a,b\}^*)^2=\{a,b\}^*$. Nov 2, 2021 at 10:44
• It could also mean pairs of words from $\{a,b\}^*$, e.g., $(abba,baaa)$. Depends on the context. Nov 2, 2021 at 11:17
• Don't forget that the empty string, $\epsilon$ is, for example, contained in $\{a,b\}^*$ so $(\{a,b\}^*)^2$ would also include $\epsilon, a$ and $b$. Nov 2, 2021 at 15:36

A string in (a, b)*, followed by another string in (a, b)*