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What Does ``No Dependence Between Instances'' Mean?

It means that there is no true dependence, anti-dependence, or output dependence between instances. Examples of these dependences are shown below:

1. True dependence: FORALL (i = 1:N) x(i) = ... ... = x(i+1) END FORALL Notice that dependences in FORALL are different from that in a DO loop. If the above example was a DO loop, that would be an anti-dependence.
2. Anti-dependence: FORALL (i = 1:N) ... = x(i+1) x(i) = ... END FORALL
3. Output dependence: FORALL (i = 1:N) x(i+1) = ... x(i) = ... END FORALL