What's the recursive definition of the heavy binary strings? Given $Σ = \{0, 1\}$ and $w ∈ Σ^*$. The binary string $w$ is called heavy if
(the number of $1$ of $w$) - (the number of $0$ of $w$) = $1$. For example, the strings $011$, $100011110$ are heavy, while the strings $0101$, $1100$, $1100100$,
$1111111$ are not.
What's the recursive definition of the heavy binary strings?

If $H$ is the set of these heavy strings, then define the basis step as $1\in H$. 
Now if $x, y$ are two strings in $H$, then the concatenations $xy$ or $yx$ will have two more $1$'s than the $0$'s. So we need to add one more zero in the string $xy$ for it to be a member of $H$. So the recursive step can be given as: if $x, y\in H$ then $0xy, x0y, xy0\in H.$
