Recursive State Machine Guided Graph Folding for Context-Free Language Reachability

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by reachable path, i.e., path whose edge labels form string accepted the given CFL. Computing expensive. The fastest algorithm exhibits slightly subcubic time complexity with respect to input size. Improving scalability practical interest, but reducing inherently difficult. In this paper, we focus on improving from more perspective---reducing Our idea arises existence trivial edges, edges that do not affect any CFL-reachability. We observe two nodes joined folded---by merging all joining them removed---without affecting result. By studying characteristic recursive state machines (RSMs), alternative CFLs, propose approach identify foldable node without need verify underlying paths (which equivalent solving problem). particular, problem instance G and RSM, based correspondence between transitions folding principle, determine adjacent examining only their incoming outgoing edges. On top efficient GF. GF linear number graph. evaluations clients (alias analysis value-flow analysis) show significantly accelerates RSM/CFL-reachability average, analysis, reduces 60.96% 42.67% graphs, obtaining speedup 4.65× memory usage reduction 57.35%. For alias 38.93% 35.61% 3.21× 65.19%.