On the non-approximability of points-to analysis

Determining points-to sets is an important static-analysis problem. Most of the classic static analyses (used e.g., by compilers or in programming environments) rely on knowing which variables might be used or defined by each expression in a program. In the presence of pointers, the use/def set of an expression like *p = *q can only be determined given (safe) points-to sets for p and q. Previous work has shown that both precise flow-sensitive and precise flow-insensitive pointer analysis is NP-Hard, even when restricted to single-procedure programs with no dynamic memory allocation. In this paper, we show that it is not even possible to compute good approximations to the precise solutions (i.e., to compute points-to sets whose sizes are within a constant factor of the sizes of the precise points-to sets) unless P=NP.