Dependence analysis for supercomputing

1. Introduction.- 2. Basic Concepts.- 2.1. Relations and Graphs.- 2.2. Orders on Vectors.- 2.3. Program Model.- 3. Dependence.- 3.1. Dependence Concepts.- 3.2. The Dependence Problem.- 4. Bounds of Linear Functions.- 4.1. Introduction.- 4.2. Bounds in Rectangles.- 4.3. Bounds in Trapezoids.- 5. Linear Diophantine Equations.- 5.1. Introduction.- 5.2. Greatest Common Divisors.- 5.3. Single Equation in Two Variables.- 5.4. Single Equation in Many Variables.- 5.5. Systems of Equations.- Appendix to Chapter 5.- 6. Dependence Tests.- 6.1. Introduction.- 6.2. One-Dimensional Arrays, Single Loops.- 6.3. One-Dimensional Arrays.- 6.4. General Case.- 6.5. Miscellaneous Comments.- References.