How can we use our decider for ?The answer here is more difficult. The new decider should first modify the input TM, M,DiscussionTMAso the modified TM, , accepts, whenever TMMhalts. Since Mis a part of the input, the modification must be apart of the computation. 211MFaithful to our principal “ If it ain’t broken don’t fix it”, the modified TM keeps Mas a subroutine, and the idea is quite simple:DiscussionLet and be the accepting and rejecting states of TM M, respectively. In the modified TM,
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