Generalized Dominance and Control Dependence

Abstract

We generalize the notion of dominance by defining a generalized dominance relation with respect to a set of paths in the control flow graph G = (V, E). This new definition leads to a generalized notion of control dependence, which includes standard control dependence and weak control dependence as special cases.If the set of paths underlying a generalized dominance relation satisfies some natural closure conditions, that dominance relation is tree-structured. Given this tree, the corresponding control dependence relation can be computed optimally by reduction to the Roman Chariots Problem, which we have developed previously for computing standard control dependence. More precisely, given linear preprocessing time and space, we can answer the (generalized version of the) so called cd, conds, and cdequiv queries in time proportional to the output of the query.To illustrate the utility of the framework, we show how weak control dependence can be computed optimally in O(|E|) preprocessing space and time. This improves the O(|V|3) time required by the best previous algorithm for this problem.