There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit goes toward infinity. Due to the halting problem, whether a word is accepted can only be determined at runtime. It can be shown by Rice's theorem, if a finite set of words are to be checked, they all have to be tested by brute force.
翻译:解决 P 和 NP 问题的尝试很多。 但是, 有了新的证明方法, P 不等于 NP 就可以被证明。 为任意的图灵机设定了时间限制, 并在超时时时拒绝输入单词 。 时间限制会持续到无穷无尽。 由于停止的问题, 一个单词是否被接受只能在运行时决定。 可以用赖斯的理论来显示, 如果要检查一组有限的单词, 它们都必须用粗力来测试 。