A unified model of a family of data flow algorithms, called elimination methods, is presented. The algorithms, which gather information about the definition and use of data in a program or a set of programs, are characterized by the manner in which they solve the systems of equations that describe data flow problems of interest. The unified model provides implementation-independent descriptions of the algorithms to facilitate comparisons among them and illustrate the sources of improvement in worst case complexity bounds. This tutorial provides a study in algorithm design, as well as a new view of these algorithms and their interrelationships.
An incremental update algorithm modifies the solution of a problem that has been changed, rather than re-solving the entire problem. ACINCF and ACINCB are incremental update algorithms for forward and backward data-flow analysis, respectively, based on our equations model of Allen-Cocke interval analysis. In addition, we have studied their performance on a "nontoy" structured programming language L. Given a set of localized program changes in a program written in L, we identify a priori the nodes in its flow graph whose corresponding data-flow equations may be affected by the changes. We characterize these possibly affected nodes by their corresponding program structures and their relation to the original change sites, and do so without actually performing the incremental updates. Our results can be refined to characterize the reduced equations possibly affected if structured loop exit mechanisms are used, either singly or together, thereby relating richness of programminglanguage usage to the ease of incremental updating.
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