Reducing the cost of data flow analysis by congruence partitioning

Abstract

Data flow analysis expresses the solution of an information gathering problem as the fixed point of a system of monotone equations. This paper presents a technique to improve the performance of data flow analysis by systematically reducing the size of the equation system in any monotone data flow problem. Reductions result from partitioning the equations in the system according to congruence relations. We present a fast O(n log n) partitioning algorithm, where n is the size of the program, that exploits known algebraic properties in equation systems. From the resulting partition a reduced equation system is constructed that is minimized with respect to the computed congruence relation while still providing the data flow solution at all program points.