Using postdomination to reduce space requirements of data flow analysis

Data Flow Analysis (DFA for short) is a basic technique to collect statical information on run-time behaviors of programs: it is essential in optimizing compilers and is also used in type inference problems [1]. When performing a DFA, the program to be analyzed is modeled by its Control Flow Graph (CFG) and by a set of transformation functions, one for each node in the graph. The set of program execution states is generally abstracted in a lattice. Each function models the effect of execution of the corresponding program instruction on the (abstracted) program execution state. Then, starting from the initial node in the CFG, and from an abstraction of the initial execution state, every possible execution path in the CFG should be tried, and the execution states encountered at each node collected. Standard DFA uses a fix point iteration to find an approximation of this information. DFA is expensive in time (because of the fixed point iteration), but also in space: a representation of the program execution state must be stored for each CFG node for the entire duration of the analysis. In this paper we propose a method to re-