Given a TM, T 1 , and any string w, there is clearly a TM, T 2 , that first screens its input to see whether it is the particular string w if it is not the input is accepted, if it is w, then T 1 is run on the input w Pictorially, Show that there is no decision procedure to determine whether any given TM (say T 2 ) accepts all strings or not Input T2 Is it w Yes 2 No Run T HALT

Question: Given a TM, T 1 , and any string w, there is clearly a TM, T 2 , that first screens its input to see

Given a TM, T₁, and any string w, there is clearly a TM, T₂, that first screens its input to see whether it is the particular string w; if it is not the input is accepted, if it is w, then T₁ is run on the input w. Pictorially,

Input T2 Is it w? Yes 2 No Run T HALT

Show that there is no decision procedure to determine whether any given TM (say T₂) accepts all strings or not.

Input T2 Is it w? Yes 2 No Run T HALT

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