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Turing reducibilityTuring reducibility

Section 6.3

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eory of Computati

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Using Turing reducibility for proingdecidability!undecidability

6.3.b Giorgi Japaridze   Theory of Computability

Theorem 6.21:

a)  f A≤TB  and B  is decidable% then A  is decidable.

!onseuently%

  b)  f A≤TB  and A  is undecidable% then B  is undecidable.

Proof (a): f B is decidable% then we may replace the oracle for B byan actual procedure that decides B. Thus we may replace the OTM

that decides A relative to B by an ordinary TM that decides A.