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I suppose not, but I do not have a clear way to prove it. Right now, I am trying to find a counter example that there exists a language that cannot be reduced from the language, but I am not sure if there is the right direction.

D.W.
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Anonny
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1 Answers1

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Every Turing-decidable language is Turing-reducable to every language.

According to the definition in Wikipedia,

Given two sets $A,B \subseteq \mathbb{N}$ of natural numbers, we say $A$ is Turing reducible to $B$ and write

$$A \leq_T B$$

if there is an oracle machine that computes the characteristic function of $A$ when run with oracle $B$.

Now if $A$ is decidable, the oracle machine can decide $A$ even without the use of the oracle, so $A$ is Turing-reducible to every language.

xskxzr
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