New results on the computability and complexity of points--to analysis

Given a program and two variables p and q, the goal of points-to analysis is to check if p can point to q in some execution of the program. This well-studied problem plays a crucial role in compiler optimization. The problem is known to be undecidable when dynamic memory is allowed. But the result is known only when variables are allowed to be structures. We extend the result to show that, the problem remains undecidable, even when only scalar variables are allowed. Our second result deals with a version of points-to analysis called flow-insensitive analysis, where one ignores the control flow of the program and assumes that the statements can be executed in any order. The problem is known to be NP-Hard, even when dynamic memory is not allowed and variables are scalar. We show that when the variables are further restricted to have well-defined data types, the problem is in P. The corresponding flow-sensitive version, even with further restrictions, is known to be PSPACE-Complete. Thus, our result gives some theoretical evidence that flow-insensitive analysis is easier than flow-sensitive analysis. Moreover, while most variations of the points-to analysis are known to be computationally hard, our result gives a rare instance of a non-trivial points-to problem solvable in polynomial time.