Problem $1(25$ points$)$: Let $M=(Q,,,q_0,(F))$ a deterministic finite automata $($DFA$)$ that

accepts the following language $L$ over the alphabet $=\{0,1\}$ :

$|)$:$\}$ has an equal number of $0\text{'}$s and $1\text{'}$s such that each prefix of $w$ has at

mostone more $1$ than $0\text{'}$s and at most one more $0$ than $1\text{'}$s