雙語暢銷書《艾倫圖靈傳》第3章:思考什麼是思考(79)
Alan had rendered the vague idea of a 'definite method' or a 'mechanical process' into something very precise: a 'table of behaviour'.
And so now he had a very precise question to answer: was there or was there not one of these machines, one of these tables, that could produce the decision that Hilbert asked for?
現在他面臨的問題非常明確：在這無數種機器（也就是行爲表）中，有沒有一個可以滿足希爾伯特的要求？An example machine: The following 'table of behaviour' completely defines a machine with the character of an adding machine.
一個機器的例子：後面的行爲表，定義了一臺加法機。
Started with the 'scanner' somewhere to the left of two groups of 1's, separated by a single blank space, it will add the two groups, and stop. Thus, it will transform into
起始時，有兩組"1"中間用一個空格隔開，掃描器位於它們的左側。這臺機器的功能，是將兩組"1"加起來，合爲一組，然後停止，也就是變成這樣：The task of the machine is to fill in the blank space, and to erase the last '1'.
這臺機器的任務，就是將空格填入“1”，並清除最後一個“1”。It will therefore suffice to provide the machine with four configurations.
它一共有4種狀態。In the first it moves along the blank tape looking for the first group of 1s.
一開始，它沿着紙帶向右移動，尋找第一個"1"，這是第一種狀態；When it moves into the first group, it goes into the second configuration.
當它找到後，它進入第二種狀態，繼續移動；The blank separator sends it into the third configuration, in which it moves along the second group until it encounters another blank, which acts as the signal to turn back, and to enter the fourth and final configuration in which it erases the last '1' and marks time for ever.
遇到空格後，它進入第三種狀態，沿着第二組移動；再遇到空格，就進入第四種狀態，清除最後一個"1"，並停機。The complete table is:
那麼完整的行爲表就是這樣的：Even a very simple machine of this kind, as shown in the example, would be doing more than sums.
像例子中這樣的最簡單的機器，就可以實現相加。The machine would effect acts of recognition, such as 'finding the first symbol to the right'.
它具有識別功能，比如“向右尋找第一個符號”。A rather more complicated machine could perform multiplication, by repeated acts of copying out one group of 1's, while erasing one at a time of another group of 1's, and recognising when it had finished..
如果再複雜一點，在逐個擦除一組"1"的同時不斷地複製另一組"1"，並且識別什麼時候該結束，就能實現乘法。Such a machine could also effect acts of decision, as for instance in deciding whether one number was divisible by another, or whether a given number was prime or composite.
這種機器也具有判斷功能，比如判斷一個數是否能被另一個數整除，或者一個數是素數還是合數。Clearly there was scope for exploiting this principle to mechanise a vast range of 'definite methods'.
很明顯，這種“機械的過程”，還有很大的拓展餘地。But could there be such a machine that could decide Hilbert's question about provability?
但問題是，這樣的機器能解決希爾伯特的可判定性問題嗎？This was much too hard a problem to approach by trying to write a 'table' to solve it.
要想通過寫出一個這樣的行爲表，來解決這個問題，這實在是太難了。
