Abstract
A simple, iterative bit propagation algorithm for solving global data flow analysis problems such as “available expressions” and “live variables” is presented and shown to be quite comparable in speed to the corresponding interval analysis algorithm. This comparison is facilitated by a result relating two parameters of a reducible flow graph (rfg). Namely, if G is an rfg, d is the largest number of back edges found in any cycle-free path in G, and k is the length of the interval derived sequence of G, then $k \geqq d$. (Intuitively, k is the maximum nesting depth of loops in a computer program, while d is a measure of the maximum loop-interconnectedness.) The node ordering employed by the simple algorithm is the reverse of the order in which a node is last visited while growing any depth-first spanning tree of the flow graph. In addition, a dominator algorithm for an rfg is presented which takes O(edges) bit vector steps.
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