Question

Nobody knows yet if P = NP. Consider the language L defined as
follows
L=(0 + 1)* if P = NP
= φ otherwise

Which of the following statements is true?
(A) L is recursive
(B) L is recursively enumerable but not recu
(C) L is not recursively enumerable
(D) Whether L is recursive or not will be known after we find out if
P = NP

Answer 1

Answer on Question#38608 – Math - Other

Regular language is a formal language that can be expressed using a regular expression. A formal language (a set of strings of symbols that may be constrained by rules that are specific to it) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language.

All regular, context-free and context-sensitive languages are recursive. Incidentally, the all recursive languages are also recursively enumerable.

So the right answer is A).