The Complexity of Type Analysis of Object Oriented Programs

One of the price tags attached to the blessings that OO brings about is a drop in efficiency due to dynamic method dispatch. Much research effort is being spent on the problem of eliminating it, by applying static analysis to predict the set of dynamic types which a variable might store at any given program location. It was previously shown that the problem is NP-hard even if the program under analysis has no multi-level pointers. In this work, we show that under similar conditions, the problem is P-SPACE complete, provided that the program is not recursive. In the presence of recursion, the problem becomes EXP-TIME complete. (These two results also give an exponential time algorithm for a family of type analysis problems.) If multi-level pointers are allowed then the problem becomes EXP-SPACE complete without recursion and DEXP-TIME with it. Further, if the program under analysis may use recursive data structures then the problem becomes undedicable. Despite these, somewhat discouraging, results, we can prove that the type analysis becomes tractable, as evident from past practical experience, if the program under analysis obeys some few simple software engineering rules, while the analysis algorithm makes a corresponding simplifying assumption.