Course Solutions Uncategorized (Solved) : 2 Prove Alltm Undecidable Modifying Proof Pre Vious Page Filling Blanks Alltm M M Tm Accep Q27305827 . . . .

(Solved) : 2 Prove Alltm Undecidable Modifying Proof Pre Vious Page Filling Blanks Alltm M M Tm Accep Q27305827 . . . .

June 27, 2024June 27, 2024| adminadmin| 0 Comment| 8:32 pm
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2. Prove that ALLTM is undecidable by modifying the proof on the pre- vious page and filling in the blanks. ALLTM = {〈 M 〉 | M is a TM which accepts every input string} Proof: For any < M, w > let M be the TM which takes as input string (a) If xメu, then M1 (b) If x = w then M Now we construct TM V to decide ATM. Let R be a hypothetical TM which decides ALLTM-V has input < M, w 〉 and does the following: (a) Uses 〈 M, w 〉 to output 〈 Mi 〉. (b) Runs R on 〈 M 〉. (c) If R accepts then If R rejects then If R decides ALLTM, then V decides ATM. Therefore R cant exist and ALLTM is undecidable.

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