Separation of Complexity Classes
Computational complexity theory is the study of the quantitative laws that govern computing. A central topic in this study is the classification of computational prob¬lems by the amount of various computational resources required for their solution and, particularly, to find the limits of feasible computation.
Computational complexity has discovered (or defined) a beautiful structure of natural, mathematically robust complexity classes that give an intuitively satisfy¬ing classification of the feasibly and near-feasibly computable problems. These complexity classes are defined by the bounds on computational resources or by the natural complete problems to which other problems in the class can be easily reduced. They can also be defined very naturally, in a noncomputational way, by the expressive power of various logical formalisms, emphasizing that they are natural, robust and important mathematical objects.
Unfortunately, notwithstanding considerable effort over several decades, there are no proofs that all these classes are indeed different. We consider the resolution of the separation questions for these complexity classes as one of the most important set of open problems in theoretical computer science. The solution of the separation problems is essential for deeper understanding of the nature of computing, the limits of feasible computation and, indirectly, the limits of feasible (axiomatic) reasoning.

分离复杂班
计算复杂性理论是研究定量治社会的法律运算。一个中心议题，在这项研究是分类计算概率行政长官是由葡萄糖的金额计算各种所需的资源，为他们的解决方案，尤其是寻找极限可行的计算方法。
计算复杂度已发现（或界定）一个美丽的结构，自然，数学上的复杂性强劲班，让大家一个直观的满足，你荷兰分类的可行性和近切实可计算问题。这些复杂班级界定范围计算资源，或由天然完整的问题，而其他问题，在课堂可以很容易地减少。他们也可以被界定，很自然的，在一个noncomputational方式所表达能力的各种逻辑formalisms强调说，他们是天然的，强大的和重要的数学对象。
不幸的是，尽管有相当大的努力，这几十年来，因此没有证据证明这些班都是确有不同。我们认为，解决分离问题，为这些复杂班级的一个最重要的一套公开的问题，在理论计算机科学。解决分离问题，是至关重要的更深的了解性质的计算，限制了可行的计算方法，并间接的界限不可行（公理化）的道理。