Nobody knows yet if P = NP. Consider the language L defined as follows : Which…

2003

Nobody knows yet if P = NP. Consider the language L defined as follows :
GATECS2003Q13
Which of the following statements is true ?

  1. A.

    L is recursive

  2. B.

    L is recursively enumerable but not recursive

  3. C.

    L is not recursively enumerable

  4. D.

    Whether L is recursive or not will be known after we find out if P = NP

Attempted by 8 students.

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Correct answer: A

The language L is defined as (0+1)* if P = NP, otherwise the empty set. Since both (0+1)* and the empty set are regular languages, they are also recursive. Therefore, regardless of whether P = NP is true or false, L is always a recursive language. This means that statement A (L is recursive) must be true.

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