对数空间下的复杂度世界

M. Liskiewicz, R. Reischuk
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引用次数: 9

摘要

研究使用小于对数空间的图灵机定义的空间复杂度类。由于这类机器的计数能力有限,大多数标准模拟技术不适用于次对数空间类。然而,只有这么小空间的机器可能仍然非常强大。因此,对于日志空间以上的类,如何获得已知的包含和分离结果的类似物并不明显。我们回顾了关于次对数空间世界的已知事实,并提出了几个新的结果,这些结果表明这些类的行为确实不同,例如某些闭包性质不成立。这些机器的有限能力使得通过组合论证证明显式分离——甚至对于交替的复杂性类——成为可能,并且在没有任何未经证明的假设的情况下获得非相对复杂性类的层次结构。我们还讨论了向上和向下的翻译问题。最后,这些复杂性类与/spl Pscr/中的其他类相关,特别是与上下文无关的语言相关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The complexity world below logarithmic space
Investigates space complexity classes defined by Turing machines that use less than logarithmic space. Because of the limited counting ability of such machines, most of the standard simulation techniques do not work for sublogarithmic space classes. However, machines with such little space may still be quite powerful. Therefore, it was not obvious how to obtain analogs for inclusion and separation results known for classes above logspace. We review known facts about the sublogarithmic space world and present several new results which show that these classes really behave differently, e.g. certain closure properties do not hold. The restricted power of these machines makes it possible to prove explicit separations-even for alternating complexity classes-by combinatorial arguments, and to obtain a hierarchy of non-relativized complexity classes without any unproven assumption. We also discuss upward and downward translation issues. Finally, these complexity classes are related to other classes within /spl Pscr/, in particular to context-free languages.<>
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