Lecture15_Part7 - Discussion It should be noted that...

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Unformatted text preview: Discussion It should be noted that modifying TM M to get M 1 , is part of TM S, the new decider for HALTTM , and can be carried out by it. It is not hard to see that S decides HALTTM . Since HALTTM is undecidable, we conclude that ATM is undecidable too. Discussion The final description of a decider S for ATM is: S="On input M , w where M is a TM: 1. Modify M as described to get M 1 . 2. Run R, the decider of HALTTM with input M1, w . 3. If R accepts - accept, otherwise - reject. " 26 25 The TM Emptiness Problem Proof Outline The proof is by reduction from ATM : 1. We know that ATM is undecidable. 2. We want to prove ETM is undecidable. 3. We assume toward a contradiction that ETM is decidable and devise a decider for ATM . 4. We conclude that ETM is undecidable. 28 We continue to demonstrate reductions by showing that the language ETM , defined by ETM = M | M is a TM And L(M ) = { } is undecidable. Theorem ETM is undecidable. 27 ...
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