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 7 章
5. 將這兩個數值編碼成適合標籤系統使用的字串。對我們的範例磁帶來說，可以使用
aa
，再跟著 26 個
bb
的副本，接著是
cc
，然後是 12 個
dd
的副本。
6. 使用簡單的數值運算（加倍、減半、遞增、遞減、奇偶數檢查）來模擬讀取磁帶的
讀取和寫入，以及磁帶頭的移動。例如，我們可以將代表左邊部分的數值加倍，並
將代表右邊部分的數值減半，就可以在我們的範例磁帶將磁帶頭往右移動
7
：26 加
倍會得到 52，也就是二進位的 110100；12 的一半是 6，也就是二進位的 110；所
以新磁帶看起來像是
011010(0)011000
。從磁帶讀取意謂著檢查代表磁帶左邊部分
的數值是偶數還是奇數，而將
1
或
0
寫入磁帶則意謂著遞增或遞減該數值。
7. 代表模擬圖靈機的目前狀態，可以選擇用於編碼左右磁帶數值的字元：或許當機器
處於狀態 1 的時候，我們用
a
、
b
、
c
、
d
字元來對磁帶編碼，但是當進入狀態 2 時，
我們就改用
e
、
f
、
g
、
h
等字元。
8. 將每條圖靈機規則轉換成以適當方式重寫目前字串的標籤系統：讀取
0
、寫入
1
、
向右移動磁帶頭並進入狀態 2 的規則可以變成檢查左邊磁帶數值是不是偶數的標籤
系統、遞增它、減半右邊磁帶數值的同時也加倍左邊磁帶數值、並且以狀態 2 的字
元產生編碼過的最終字串。
9. 合併這些個別的標籤系統，製作出可以模擬圖靈機每條規則的大型系統。
圖靈機的標籤系統模擬物如何運作的完整說明，請見馬修 • 庫克（Matthew
Cook）這篇文件（
http://www.complex-systems.com/pdf/15-1-1.pdf ...
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