稳健模拟和显著分离
Robust Simulations and Significant Separations
摘要：
我们定义和研究了一个新的概念之间的复杂性类，这是中间的传统概念的无限经常和几乎无处不在，以及相应的概念“显着分离”的“鲁棒模拟”。语言L在复杂性类C中具有鲁棒模拟，如果在C中存在一种语言，其在输入长度的任意大多项式延伸上与L一致。如果在C中没有对L的鲁棒模拟，则L与C存在显著分离。模拟的新概念是一个比无限经常概念更清晰和更自然的模拟概念。我们表明，复杂性理论中的各种影响，如PH的崩溃，如果NP = P和卡普-利普顿定理具有类似的强大的模拟。然后，我们使用这些结果来证明，在复杂性理论，如层次定理，固定的多项式电路下界，时空权衡，和定理的Allender和Williams，最已知的分离，可以加强到显着的分离，虽然在每种情况下，几乎无处不在的分离是未知的。证明我们的结果需要几个新的想法，包括一个完全不同的证明非确定性多项式时间比以前已知的层次定理。
英文摘要：
We define and study a new notion of "robust simulations" between complexity classes which is intermediate between the traditional notions of infinitely-often and almost-everywhere, as well as a corresponding notion of "significant separations". A language L has a robust simulation in a complexity class C if there is a language in C which agrees with L on arbitrarily large polynomial stretches of input lengths. There is a significant separation of L from C if there is no robust simulation of L in C. The new notion of simulation is a cleaner and more natural notion of simulation than the infinitely-often notion. We show that various implications in complexity theory such as the collapse of PH if NP = P and the Karp-Lipton theorem have analogues for robust simulations. We then use these results to prove that most known separations in complexity theory, such as hierarchy theorems, fixed polynomial circuit lower bounds, time-space tradeoffs, and the theorems of Allender and Williams, can be strengthened to significant separations, though in each case, an almost everywhere separation is unknown. Proving our results requires several new ideas, including a completely different proof of the hierarchy theorem for non-deterministic polynomial time than the ones previously known.
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