Taming transitive redundancy for context-free language reachability

Given an edge-labeled graph, context-free language reachability (CFL-reachability) computes reachable node pairs by deriving new edges and adding them to the graph. The redundancy that limits scalability of CFL-reachability manifests as redundant derivations, i.e., identical can be derived multiple times due many paths between two nodes. We observe most arises from derivations involving transitive relations pairs. Unfortunately, existing techniques for reducing in transitive-closure-based problems are either ineffective or inapplicable identifying eliminating during on-the-fly solving. This paper proposes a scalable yet precision-preserving approach all-pairs analysis taming its redundancy. Our key insight is intrinsically ordered, utilizing order edge derivation avoid To address challenges determining dynamically changed graph solving, we introduce hybrid representation combining spanning trees adjacency lists, together with dynamic construction algorithm. Based on this representation, propose fast effective partially ordered algorithm POCR boost performance experiments context-sensitive value-flow field-sensitive alias C/C++ demonstrate promising POCR. On average, eliminates 98.50% 97.26% respectively analysis, achieving speedups 21.48× 19.57× over standard also compare recent open-source tools, Graspan (a solver) Soufflé Datalog engine). results 3.67× faster than average both analysis.