Modern processors use cache memory, a memory access that “hits” the cache returns early, while a “miss” takes more time. Given a memory access in a program, cache analysis consists in deciding whether this access is always a hit, always a miss, or is a hit or a miss depending on execution. Such an analysis is of high importance for bounding the worst-case execution time of safety-critical real-time programs. There exist multiple possible policies for evicting old data from the cache when new data are brought in, and different policies, though apparently similar in goals and performance, may be very different from the analysis point of view. In this article, we explore these differences from a complexity-theoretical point of view. Specifically, we show that, among the common replacement policies, Least Recently Used is the only one whose analysis is NP-complete, whereas the analysis problems for the other policies are PSPACE-complete.

中文翻译：

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不同替换策略下缓存分析的复杂性

现代处理器使用高速缓存，“命中”高速缓存的内存访问会提前返回，而“未命中”则需要更多时间。给定程序中的内存访问，缓存分析包括确定此访问是否总是命中、总是未命中，或者取决于执行是命中还是未命中。这种分析对于限制安全关键实时程序的最坏情况执行时间非常重要。当引入新数据时，存在多种可能的从缓存中驱逐旧数据的策略，并且不同的策略虽然在目标和性能上看起来相似，但从分析的角度来看可能会有很大的不同。在本文中，我们从复杂性理论的角度探讨这些差异。具体来说，我们表明，在常见的替代政策中，