Unformatted text preview: Demonstration
Consider
HALTTM = M , w  M is a TM that halts on w The "Real" Halting Problem
{ } Theorem
HALTTM is undecidable. 3. We assume that B is decidable and use this assumption to prove that A is decidable. In the following slides we assume (towards a contradiction) that HALTTM is decidable and use this assumption to prove that ATM is decidable. Proof By reducing HALTTM to ATM .
10 4. We conclude that B is undecidable. 9 Discussion Discussion
Recall the definition of ATM :
ATM = M , w  M is a TM that accepts w Assume by way of contradiction that HALTTM is decidable. { }
Why is it impossible to decide ATM ? Because as long as M runs, we cannot determine whether it will eventually halt. Well, now we can, using the decider R for HALTTM .
12 Recall that a decidable set has a decider R: A TM that halts on every input and either accepts or rejects, but never loops!. We will use the assumed decider of HALTTM to devise a decider for ATM . 11 ...
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 Winter '99
 Paturi
 Halting problem, Undecidable problem, HALTTM

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