Detection of infeasible paths using Presburger arithmetic

Abstract

Detecting infeasible paths (IFPs) allows accurate computation of various kinds of program slices, and accurate detection of semantic errors that may occur when two variants of a program are merged. We propose a method of efficiently determining the truth of a prenex normal form Presburger sentence (P-sentence) bounded only by existential quantifiers, which is suitable for detecting IFPs. In this method, a coefficients matrix is converted into a triangular matrix based on the method proposed by Cooper (1972). If the rank of the matrix is lower than the degree of the matrix, the matrix is triangulated by using a method for solving one linear equation with three or more unknowns, so that the matrix can be back-substituted. This paper shows that an implementation of our method provides a slower increase in computation time than the previous method and reduces computation time by up to 3,000,000 times.