# Fast and exact analysis for LRU caches

arXiv: https://arxiv.org/abs/1811.01670 · HTML: https://mlsanity.com/paper/1811.01670/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Cost-Efficient Large Language Model Serving for Multi-turn Conversations with CachedAttention](https://mlsanity.com/paper/2403.19708/) (2024)
- [Echo: Efficient Co-Scheduling of Hybrid Online-Offline Tasks for Large Language Model Serving](https://mlsanity.com/paper/2504.03651/) (2025)
- [Deconstructing Subset Construction -- Reducing While Determinizing](https://mlsanity.com/paper/2505.10319/) (2025)

## Abstract (arXiv)

For applications in worst-case execution time analysis and in security, it is desirable to statically classify memory accesses into those that result in cache hits, and those that result in cache misses. Among cache replacement policies, the least recently used (LRU) policy has been studied the most and is considered to be the most predictable. The state-of-the-art in LRU cache analysis presents a tradeoff between precision and analysis efficiency: The classical approach to analyzing programs running on LRU caches, an abstract interpretation based on a range abstraction, is very fast but can be imprecise. An exact analysis was recently presented, but, as a last resort, it calls a model checker, which is expensive. In this paper, we develop an analysis based on abstract interpretation that comes close to the efficiency of the classical approach, while achieving exact classification of all memory accesses as the model-checking approach. Compared with the model-checking approach we observe speedups of several orders of magnitude. As a secondary contribution we show that LRU cache analysis problems are in general NP-complete.