Let s be a recursive decidable set what can we say

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Unformatted text preview: hence rec. 2/23/14 © UCF EECS 5 Sample Ques+on#6 6.  Assuming TOTAL is undecidable, use reduc+on to show the undecidability of Incr = { f | ∀x ϕf (x+1) > ϕf (x) } Let f be arb. Define Gf (x) = ϕf (x) - ϕf (x) + x f ∈ TOTAL iff ∀xϕf (x)↓ iff ∀x Gf(x)↓ iff ∀x ϕf (x) - ϕf (x) + x = x iff Gf ∈ Incr 2/23/14 © UCF EECS 6 Sample Ques+on#7 7. Let Incr = { f | ∀x, ϕf(x+1)>ϕf(x) }. Let TOT = { f | ∀x, ϕf(x)↓ }. Prove that Incr ≡m TOT. Note Q#6 starts this one. Let f be arb. Define Gf (x) = ∃t[stp(f,x,t) && stp(f,x+1,t) && (value(f,x+1,t) > value(f,x,t))] f ∈ Incr iff ∀x ϕf(x+1)>ϕf(x) iff...
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This document was uploaded on 03/29/2014 for the course COT 6410 at University of Central Florida.

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