Optimization of the Context-Free Language Reachability Matrix-Based Algorithm

Abstract

Various static analysis problems are reformulated as instances of the Context-Free Language Reachability (CFL-r) problem. One promising way to make solving CFL-r more practical for large-scale interprocedural graphs is to reduce CFL-r to linear algebra operations on sparse matrices, as they are efficiently executed on modern hardware. In this work, we present five optimizations for a matrix-based CFL-r algorithm that utilize the specific properties of both the underlying semiring and the widely-used linear algebra library SuiteSparse:GraphBlas. Our experimental results show that these optimizations result in orders of magnitude speedup, with the optimized matrix-based CFL-r algorithm consistently outperforming state-of-the-art CFL-r solvers across four considered static analyses.