On the Complexity of Cache Analysis for Different Replacement Policies

Abstract

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.