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Question

Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 iff f(x) ∈ L2]. Further, let f^-1 be also polynomial time computable. Which of the following CANNOT be true?

a.

L1 ∈ P and L2 is finite

b.

L1 ∈ NP and L2 ∈ P

c.

L1 is undecidable and L2 is decidable

d.

L1 is recursively enumerable and L2 is recursive

Answer: (c).L1 is undecidable and L2 is decidable

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Q. Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 iff f(x) ∈ L2]. Further, let f^-1 be also...

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