November 2017
Beginner to intermediate
344 pages
7h 2m
Chinese
Content preview from 深入理解運算原理｜從簡單的機器到無所不能的程式
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第 8 章
• 有時會出現錯誤的答案，例如即使
do_the_opposite.rb
停止，也預測它會永久循環
（反之亦然）。
• 有時會永遠循環，而且絕不會傳回任何答案，就像
#evaluate
在
rruby does_it_say_
no.rb < does_it_say_no.rb
裡所完成的。
所以完全正確執行
#halts?
也就永遠不可能存在：輸入必須造成不正確的預測或完全沒
有預測。
記住可決定性的定義：
如果有一種演算法保證能在有限的時間內解決任何可能的輸入，則決定性問題
就是可以決定的。
我們已經證明不可能編寫出可以完全解決停機問題的 Ruby 程式，且由於 Ruby 程式的
運算能力和圖靈機器相當，所以圖靈機也是不可能。邱奇 - 圖靈論題提及，每個演算法
都可以由圖靈機執行，所以如果沒有解決停機問題的圖靈機，也就沒有演算法；也就是
說，停機問題是無法決定的。
其他無法決定的問題
讓人氣餒的是，電腦無法確實解決容易定義的問題（『這個程式該停止嗎？』）。然而，
這是個相對抽象的具體問題，而我們用來描述它的
do_the_opposite.rb
程式既不切實
際、又做作不自然；我們似乎不可能一直想要真的實作
#halts?
，或者編寫像是
do_the_
opposite.rb
的程式，作為真實世界應用程式的一部分。也許我們可以忽視無法決定作為
學術上的好奇心，並且繼續過我們的日子。
不幸的是，這並非那麼簡單，因為停機問題不是無法決定唯一的問題。在我們建置軟體
的日常工作當中，可能實際想要解決其他諸多問題，而這些問題的無法決定性，對自動 ...
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