1
$\begingroup$

Let $B = \{ 123 \}$.

Note that $B$ is finite.

Let $L = \left \{ \left\langle M \right\rangle | M \text{ is a Turing machine such that } B \subseteq L(M) \right\}$.

Is it sufficient to show that $L$ is recognizable by checking if $M$ accepts on input $123$, and therefore $\left\langle M \right\rangle \in L$?

$\endgroup$

1 Answer 1

1
$\begingroup$

Yes, it is sufficient.

$\langle M \rangle \in L \Longleftrightarrow B\subseteq L(M) \Longleftrightarrow M\text{ accepts all strings in }B \Longleftrightarrow M\text{ accepts }123$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.