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Which of the following problems are decidable? 1) Does a given program ever produce an output? 2) If L is a context-free language, then is L̄ also context-free? 3) If L is a regular language, then is L̄ also regular? 4) If L is a recursive language, then is L̄ also recursive?

1. 1, 2, 3, 4
2. 1, 2
3. 2, 3, 4
4. 3, 4

Correct answer: 3, 4

Solution

Options 3 and 4 are correct because the complement of a regular language is always regular, and the complement of a recursive language is also recursive, making both problems decidable. In contrast, the other options involve undecidable problems.

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