Regular expression for the language accepting the strings containing at most one pair of $1$'s over $\{0,1\}$
The logic behind $(11+\epsilon)$ is to either allow a $11$, or allow no such pairs. The question states &quot;[...] containing at most one pair [...]&quot;, and therefore we need to allow either one or zero pairs, and this is achieved by $(11+\epsilon)$.