使用自动归约法分离复杂性类
Separating complexity classes using autoreducibility
摘要：
一个集合是自动可约的，如果它可以被一个不向预言机询问自己的输入的图灵机约化为它自己。我们使用autoreducational分离的多项式时间层次从多项式空间表明，所有图灵完备集的某些水平的指数时间层次是autoreducational，但存在一些图灵完备集的双指数空间，是不是。虽然我们已经知道如何使用对角化来分离这些类，但我们的证明仅通过显示它们具有不同的结构属性来分离类，从而将Post的程序应用于复杂性理论。我们认为这种技术可能在未来证明未知的分离。特别是，如果我们能够解决双指数时间的所有图灵完备集是否都是自可约的问题，我们就可以将多项式时间与多项式空间分离，将非确定性对数空间与非确定性多项式时间分离，或者将多项式时间层次与指数时间分离。我们还研究了非自适应、有界查询、概率和非均匀约简下的完备集自动约简。我们展示了如何解决这些自动归约问题也将阅读到新的复杂性类分离。
英文摘要：
A set is autoreducible if it can be reduced to itself by a Turing machine that does not ask its own input to the oracle. We use autoreducibility to separate the polynomial-time hierarchy from polynomial space by showing that all Turing-complete sets for certain levels of the exponential-time hierarchy are autoreducible but there exists some Turing-complete set for doubly exponential space that is not. Although we already knew how to separate these classes using diagonalization, our proofs separate classes solely by showing they have different structural properties, thus applying Post's Program to complexity theory. We feel such techniques may prove unknown separations in the future. In particular, if we could settle the question as to whether all Turing-complete sets for doubly exponential time are autoreducible, we would separate either polynomial time from polynomial space, and nondeterministic logarithmic space from nondeterministic polynomial time, or else the polynomial-time hierarchy from exponential time. We also look at the autoreducibility of complete sets under nonadaptive, bounded query, probabilistic and nonuniform reductions. We show how settling some of these autoreducibility questions will also read to new complexity class separations.
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