We assume that the reader is familiar with relations and their graphs. The first section of this chapter gives some of the elementary definitions in this area; for more detail, consult any standard books on set theory and graph theory. We would recommend [Halmos 1965] for relations and [Knuth 1974] for graphs. Order relations on vectors are studied in Section 2.2; they are useful in understanding the ordering of loop iterations which plays a very important role in dependence analysis. We introduce direction vectors in the same section and show how they represent those relations. Finally, Section 2.3 describes the program model we are going to use; the goal here is to establish notation for various loop nests containing assignment statements in the program.
KeywordsPartial Order Direction Vector Total Order Dependence Analysis Assignment Statement
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