Interprocedural Dataflow Analysis via Graph Reachability

This paper shows how a large class of interprocedural dataflow-analysis problems can be solved precisely in polynomial time. The only restrictions are that the set of dataflow facts is a finite set, and that the dataflow functions distribute over the confluence operator (either union or intersection). This class of problems includes—but is not limited to—the classical separable problems (also known as “gen/kill” or “bit-vector” problems)—e.g., reaching definitions, available expressions, and live variables. In addition, the class of problems that our techniques handle includes many non-separable problems, including trulylive variables, copy constant propagation, and possibly-uninitialized variables. A novel aspect of our approach is that an interprocedural dataflow-analysis problem is transformed into a special kind of graph-reachability problem (reachability along interprocedurally realizable paths). The paper presents three polynomial-time algorithms for the realizable-path reachability problem: an exhaustive version, a second exhaustive version that may be more appropriate in the incremental and/or interactive context, and a demand version. The first and third of these algorithms are asymptotically faster than the best previously known realizable-path reachability algorithm. An additional benefit of our techniques is that they lead to improved algorithms for two other kinds of interproceduralanalysis problems: interprocedural flow-sensitive side-effect problems (as studied by Callahan) and interprocedural program slicing (as studied by Horwitz, Reps, and Binkley).