On the Difference Between One and Many (Preliminary Version)
On the Difference Between One and Many (Preliminary Version)
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论一与多的区别（初稿）
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发表时间：
1977
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通讯作者：
Janos Simon
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作者：
Janos Simon
我们研究了以下问题：‘给定一个问题，判断这个问题有多少个解决方案比仅仅判断它是否有解决方案更难？’我们表明，在特定情况下，问题可以用一种数学上有意义的形式来表示，即我们何时可以将“解的数量”转换为“非确定图灵机的不同接受计算的数量”(可能带有适当的权重)。在这个背景下，正如我们所展示的，这些问题等同于关于概率机器的问题(在Gill(9)的意义上)。
We examine the following question: ‘Given a problem, is it more difficult to tell how many solutions the problem has than just deciding whether it has a solution?’. We show, that in specific cases, the question can be put into a mathematically meaningful form, namely when we can translate ‘number of solutions’ as ‘number of distinct accepting computations of a nondeterministic Turing machine’ (perhaps with appropriate weights). In this context, as we show, these questions are equivalent to problems about probabilistic machines (in the sense of Gill (9)).