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Unformatted text preview: recall the halting problem We showed that H is uncomputable by reducing navel_gaze to H . def H(f, i): Return True if f(i) will halt, False otherwise. # Once youve figured out how to implement this, delete next line return True def navel_gaze(f) : if H(f, f) : while True : pass else : print "f(f) didnt halt!" Clearly navel_gaze(navel_gaze) is uncomputable: it halts if, and only if, it doesn't halt. One way to proceed is to say that the uncomputability of navel_gaze implies the uncomputability of H . A more direct route is through the contrapositive: the computability of H would imply the computability of navel_gaze , because we can reduce navel_gaze to H . . . contradiction! navel_gaze reduces to H : use the second to implement the rst. slide 2 another reduction Once we have shown that H is uncomputable we can use a reduction to show that some other problems are uncomputable. The idea is that if we can use some function f to implement H , then H is no harder to solve than...
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This note was uploaded on 10/13/2011 for the course COMPUTER S CSC 165 taught by Professor Dannyheap during the Fall '10 term at University of Toronto- Toronto.
- Fall '10
- Computer Science