This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
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
 DannyHeap
 Computer Science

Click to edit the document details