The computational complexity of polynomial time problems

点击翻译按钮获取中文摘要

Complexity theory aims at rigorously classifying problems solvable by computers on the basis of the amounts of resources needed to solve them. Computing time is considered as a resource, as well as memory, processors, random bits, communication bits, etc. The methodology of complexity theory rests on the definition of abstract computer models, on the development of algorithms solving a problem on such models, and (ideally) on the mathematical proof that the algorithms found are the best possible. In some cases, such a proof would have great practical value; for example, the security of cryptographic protocols in actual use today rests on the perceived --but as yet unproven-- difficulty of computational problems such as factoring a large number into two smaller numbers that multiply out to this number.