Context-free language (CFL) reachability is a fundamental framework for formulating program analyses. CFL-reachability analysis works on top of an edge-labeled graph by deriving reachability relations and adding them as labeled edges to the graph. Existing CFL-reachability algorithms typically adopt a single-reachability relation derivation (SRD) strategy, i.e., one reachability relation is derived at a time. Unfortunately, this strategy can lead to redundancy, hindering the efficiency of the analysis. To address this problem, this paper proposes Pearl , a multi-derivation approach that reduces derivation redundancy for CFL-reachability solving, which significantly improves the efficiency of CFL-reachability analysis. Our key insight is that multiple edges can be simultaneously derived via batch propagation of reachability relations. We also tailor our multi-derivation approach to tackle transitive relations that frequently arise when solving CFL-reachability. Specifically, we present a highly efficient transitive-aware variant, Pearl^PG , which enhances Pearl with propagation graphs , a lightweight but effective graph representation, to further diminish redundant derivations. We evaluate the performance of our approach on two clients, i.e., context-sensitive value-flow analysis and field-sensitive alias analysis for C/C++. By eliminating a large amount of redundancy, our approach outperforms two baselines including the standard CFL-reachability algorithm and a state-of-the-art solver Pocr specialized for fast transitivity solving. In particular, the empirical results demonstrate that, for value-flow analysis and alias analysis respectively, Pearl^PG runs 3.09 $\times$ faster on average (up to 4.44 $\times$ ) and 2.25 $\times$ faster on average (up to 3.31 $\times$ ) than Pocr , while also consuming less memory.

中文翻译：

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Pearl：高效求解 CFL 可达性的多推导方法


上下文无关语言 (CFL) 可达性是制定程序分析的基本框架。 CFL 可达性分析在边标记图的基础上进行，通过导出可达性关系并将其作为标记边添加到图中。现有的CFL可达性算法通常采用单可达性关系推导(SRD)策略，即一次推导一个可达性关系。不幸的是，这种策略可能会导致冗余，从而降低分析的效率。针对这一问题，本文提出了Pearl ，一种多导数方法，减少了CFL可达性求解的导数冗余，显着提高了CFL可达性分析的效率。我们的主要见解是，可以通过可达性关系的批量传播同时导出多个边。我们还定制了多推导方法来解决解决 CFL 可达性时经常出现的传递关系。具体来说，我们提出了一种高效的传递感知变体Pearl ^PG ，它通过传播图（一种轻量级但有效的图表示）增强了Pearl ，以进一步减少冗余推导。我们评估了我们的方法在两个客户端上的性能，即 C/C++ 的上下文敏感值流分析和字段敏感别名分析。通过消除大量冗余，我们的方法优于两个基线，包括标准 CFL 可达性算法和专门用于快速传递性求解的最先进的求解器Pocr 。 特别是，实证结果表明，对于价值流分析和别名分析， Pearl ^{PG 的}平均运行速度平均快 3.09 $\times$（高达 4.44 $\times$），平均快 2.25 $\times$（高达 4.44 $\times$）。比Pocr低至 3.31 $\times$ ），同时消耗的内存也更少。