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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.