Show that the following language L with alphabet $\backslash$Sigma $=\{0,1\}$ is Turing$-$recognizable, but

without using a Turing machine:

L $=\{$w $|$ no prefix of w has more $0$s than $1$s$\}.$

Make sure to provide details regarding why$/$how your argument and any constructions involved

work.

Remember that a $($non$-$empty$)$ string x is a prefix of w if a string z exists such that xz $=$ w$.$

Therefore, this language contains strings such as $1100,1010,$ or $1110,$ but it does not contain strings

$01111($because of prefix $0),1001($because of prefix $100),$ or $10100($because of prefix $10100)$