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I would like to run the following string $w=011101$ on the following NTM and figure out the respective computation branches and whether it accepts or rejects that string.

$\text{Start: }(q_0) 011101 $

$0(q_3)11101$

$(q_1)011101$

$a) 0(q_{rej}) 11101 \:\:\: b) 0(q_{acc}) 11101$

My questions are:

  • Does the T.M continues on $b) 0(q_acc) 11101$ and reads a $1$, thus going to $q_2$ or it halts whenever it hits an accepting or rejecting state?
  • Does the T.M accept the string above?

NTM

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  • $\begingroup$ It does both, or it does whichever one eventually leads to an accepting state, depending on your interpretation. Since q_reject never leads to an accepting state we can ignore that branch unless it's the only branch left. $\endgroup$
    – user253751
    Aug 31 at 9:40
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The final states of a Turing machine (deterministic or not) have immediate effect and terminate the current computation. In your example, you have two final states $q_{acc}$ and $q_{rej}$ which will terminate any computation that reaches one of those state.

Now since there exists a computation that reaches the state $q_{acc}$, your non-deterministic Turing machine will terminate and accept the input. Therefore, your input $w = 011101$ will be accepted.

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