Choose the correct statement regarding decidability:

• I – A string belongs to a regular language, CFL, CSL, Recursive language, and Recursively enumerable languages is decidable.
• II – Finiteness of CSL is decidable.
• III – Emptiness of CFL and CSL is not decidable.
• IV – Emptiness of regular language and CFL is decidable.

(A) I, II and III
(B) II, III and IV
(C) Only I
(D) Only IV


Answer: (D)

Explanation:

1. Membership of regular language, CFL, CSL, and Recursive language is decidable but for RE it is not decidable.
2. Finiteness of CSL is not decidable.
3. The emptiness of CFL is decidable but for CSl it is undecidable.
4. The emptiness of regular language and CFL is decidable.

So, option (D) is correct.

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