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Unformatted text preview: Discussion
Faithful to our principal " If it ain't broken don't fix it", the modified TM keeps M as a subroutine, and the idea is quite simple: Let qaccept and qreject be the accepting and rejecting states of TM M, respectively. In the modified TM, M 1 , qaccept and qreject are kept as ordinary states.
22 Discussion How can we use our decider for ATM ? The answer here is more difficult. The new decider should first modify the input TM, M, so the modified TM, M 1 , accepts, whenever TM M halts. Since M is a part of the input, the modification must be a part of the computation. 21 Discussion
M1 Discussion We continue the modification of M by adding a new accepting sate nqaccept . Then we add two new transitions: A transition from qaccept to nqaccept , and another transition from qreject to nqaccept . M qaccept nqaccept
qreject This completes the description of M 1 . It is not hard to verify that M 1 accepts iff M halts.
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This note was uploaded on 04/30/2009 for the course CSE 105 taught by Professor Paturi during the Winter '99 term at UCSD.
- Winter '99