Alan had rendered the vague idea of a 'definite method' or a 'mechanical process' into something very precise: a 'table of behaviour'.
现在，艾伦已经将“机械的过程”这个模糊的概念，演绎成了非常严密的一张“行为表”。
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?
现在他面临的问题非常明确：在这无数种机器（也就是行为表）中，有没有一个可以满足希尔伯特的要求？
An example machine: The following 'table of behaviour' completely defines a machine with the character of an adding machine.
一个机器的例子：后面的行为表，定义了一台加法机。
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
起始时，有两组"1"中间用一个空格隔开，扫描器位于它们的左侧。这台机器的功能，是将两组"1"加起来，合为一组，然后停止，也就是变成这样：
The task of the machine is to fill in the blank space, and to erase the last '1'.
这台机器的任务，就是将空格填入“1”，并清除最后一个“1”。
It will therefore suffice to provide the machine with four configurations.
它一共有4种状态。
In the first it moves along the blank tape looking for the first group of 1s.
一开始，它沿着纸带向右移动，寻找第一个"1"，这是第一种状态；
When it moves into the first group, it goes into the second configuration.
当它找到后，它进入第二种状态，继续移动；
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.
遇到空格后，它进入第三种状态，沿着第二组移动；再遇到空格，就进入第四种状态，清除最后一个"1"，并停机。
The complete table is:
那么完整的行为表就是这样的：
Even a very simple machine of this kind, as shown in the example, would be doing more than sums.
像例子中这样的最简单的机器，就可以实现相加。
The machine would effect acts of recognition, such as 'finding the first symbol to the right'.
它具有识别功能，比如“向右寻找第一个符号”。
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..
如果再复杂一点，在逐个擦除一组"1"的同时不断地复制另一组"1"，并且识别什么时候该结束，就能实现乘法。
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.
这种机器也具有判断功能，比如判断一个数是否能被另一个数整除，或者一个数是素数还是合数。
Clearly there was scope for exploiting this principle to mechanise a vast range of 'definite methods'.
很明显，这种“机械的过程”，还有很大的拓展余地。
But could there be such a machine that could decide Hilbert's question about provability?
但问题是，这样的机器能解决希尔伯特的可判定性问题吗？
This was much too hard a problem to approach by trying to write a 'table' to solve it.
要想通过写出一个这样的行为表，来解决这个问题，这实在是太难了。