Two Birds with One Stone: Multi-Derivation for Fast Context-Free Language Reachability Analysis

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 transitive relations that frequently arise when solving reachability relations, significantly improving the efficiency of CFL-reachability analysis. Our key insight is that multiple edges involving transitivity can be simultaneously derived via batch propagation of reachability relations on the transitivity-aware subgraphs that are induced from the original edge-labeled graph. We evaluate the performance of Pearl 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, Pearl achieves average speedups of 82.73x for value-flow analysis and 155.26x for alias analysis over the standard CFL-reachability algorithm. The comparison with Pocr, a state-of-the-art CFL-reachability solver, shows that Pearl runs 10.1x (up to 29.2x) and 2.37x (up to 4.22x) faster on average respectively for value-flow analysis and alias analysis with less consumed memory.