Lecture15_Part9

Lecture15_Part9 - M1 Description of___ Proof nqaccept Now...

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Unformatted text preview: M1 Description of___ Proof nqaccept Now we add a filter to divert all inputs but w. M1 x == w filter M Therefore, M 1 satisfies: {w} if M accepts w L(M 1 ) = if M rejects w nqreject qaccept TM M 1 has a filter that rejects all inputs excepts w, so the only input reaching M, is w. yes x=w nqstart qstart qreject no xw {w} if M accepts w L(M 1 ) = if M rejects w 34 33 Proof Proof Here is a formal description of M 1 : M 1 = "On input x : 1. If x w - reject . 2. If x = w - run M on w and accept if M accepts. " Note: M accepts w if and only if L(M 1 ) . This way, if R accepts, S "can be sure" that w L(M ) and accept. Note that S gets the pair M , w as input, thus before S runs R, it should compute an encoding M 1 of M 1 . This encoding is not too hard to compute using S's input M , w . 35 36 ...
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