ADF A $=\{<$ M$,$ w $>|$ M is a DFA, w is a string, and M accepts w$\}$

$($In other words, there exists an algorithm that can take any DFA M and any string w as input

and can always correctly answer the question of whether or not M accepts w$.)$

Consider the language A$3$DF A $=\{<$ M $>|$ M is a DFA, and M accepts at least one string

x in $\{0,1\}$

$$

that has a length of $3\}.$

For example, if we pass the DFA below as input, it should be accepted because the DFA accepts

the string $011($as well as some other strings of length $3).$