Schedulability analysis for hard real-time systems requires bounds on the execution times of its tasks. To obtain useful bounds in the presence of caches, cache analysis is mandatory.The subject-matter of this article is the static analysis of the tree-based PLRU cache replacement policy (pseudo least-recently used), for which the precision of analyses lags behind those of other policies. We introduce the term subtree distance, which is important for the update behavior of PLRU and closely linked to the peculiarity of PLRU that allows cache contents to be evicted in "logarithmic time". Based on an abstraction of subtree distance, we define a must-analysis that is more precise than prior ones by excluding spurious logarithmic-time eviction.
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