Heterogeneous fixed points with application to points-to analysis

Abstract

Many situations can be modeled as solutions of systems of simultaneous equations. If the functions of these equations monotonically increase in all bound variables, then the existence of extremal fixed point solutions for the equations is guaranteed. Among all solutions, these fixed points uniformly take least or greatest values for all bound variables. Hence, we call them homogeneous fixed points. However, there are systems of equations whose functions monotonically increase in some variables and decrease in others. The existence of solutions of such equations cannot be guaranteed using classical fixed point theory. In this paper, we define general conditions to guarantee the existence and computability of fixed point solutions of such equations. In contrast to homogeneous fixed points, these fixed points take least values for some variables and greatest values for others. Hence, we call them heterogeneous fixed points. We illustrate heterogeneous fixed point theory through points-to analysis.