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为什么这个图灵机不是决策者？

[英]Why is this Turing Machine not a decider?

原文 2022-12-12 09:06:34 6 1 automata/ turing-machines

Like I get that a Turing Machine is a decider if it halts for every input .就像我知道图灵机是否在每次输入时都停止一样是决定者。 But for this question, it just gave me this diagram and asked me to deduce whether this Turing Machine was considered a decider or not and the answer was no.但是对于这个问题，它只是给了我这张图，让我推断这个图灵机是否被认为是一个决策者，答案是否定的。 How was 'no' deduced? “不”是怎么推导出来的？ I can't seem to wrap my head around this whole decider and non-decider Turing Machine thing.我似乎无法理解这整个决策者和非决策者图灵机的事情。 If anyone could help explain this to me.如果有人能帮我解释一下。 Thanks.谢谢。

1 个解决方案

If I am getting this right, then if I write "ba" on the tape and start the Turing machine with the head located at "b", then it will loop forever.如果我做对了，那么如果我在磁带上写“ba”并启动磁头位于“b”的图灵机，那么它将永远循环。

Starting at position 0 in state 0.从 state 0 中的 position 0 开始。
Read "b", replace "b" by "b", go right to position 1, move to state 1读“b”，把“b”换成“b”，go右移到position 1，移动到state 1
Read "a", replace "a" by "a", go left to position 0, move to state 0读“a”，把“a”换成“a”，go左移到position 0，移动到state 0
Read "b", replace "b" by "b", go right to position 1, move to state 1读“b”，把“b”换成“b”，go右移到position 1，移动到state 1
Read "a", replace "a" by "a", go left to position 0, move to state 0读“a”，把“a”换成“a”，go左移到position 0，移动到state 0
Read "b", replace "b" by "b", go right to position 1, move to state 1读“b”，把“b”换成“b”，go右移到position 1，移动到state 1
Read "a", replace "a" by "a", go left to position 0, move to state 0读“a”，把“a”换成“a”，go左移到position 0，移动到state 0
... ...

You can see that this will loop forever.你可以看到这将永远循环。 Because there is an input for which the Turning machine doesn't halt, it's not a decider.因为存在 Turning machine 不会停止的输入，所以它不是决策者。