Self thought

Question

We know that Regular languages are decidable under membership property and lets say $L$ is such a regular language. From Chomsky hierarchy we know that $\text{Regular languages}$ $\subset$ $\text{Recursively Enumerable Languages}$.

Lets say there are two persons $A$ and $B$ where $A$ has $\text{Regular Language}$ and person $B$ has Turing Machine $M$. Now the person $A$ do not want to specify what kind of language is $L$ before giving it to person $B$ to test whether $L$ will be accepted by machine $M$ or will go into infinite loop. Then how can we conclude that $M$ will halt after processing $L$ or will not halt at all.

Please explain with reason?

Comments

@Arjun

We can use $\text{Dovetailing}$ here to feed all the strings in $L$ to $M$.

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When will dovetailing stop?

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Yes there is no way we can find out whether $M$ will ever stop or not.