Some basic properties of unfolding are discussed in this section. These properties are useful when applications of unfolding are considered in Section 5.5.

This property is based on the fact that the sum of the delays on the *J* unfolded edges *U*_{i} → *V*_{(i+w)%J}, *i* = 0,1, ... , *J* − 1, is same as the number of delays on the edge *U* → *V* in the original DFG. Mathematically, this can be stated as

The proof of this is left as an exercise (see Problem 3). This property can be observed in Figs. 5.2, 5.3, and 5.4.

It is interesting to observe what happens when a loop is unfolded. Let *l* be a loop with *w*_{l} delays in the original DFG, and let *A* be a node in *l*. The loop *l* can be denoted as the path *A* *A* with *w*_{l} delays. If the loop *l* is traversed *p* times (*p* ≥ 1), this results in the path *A* *A* ... *A* with *pw*_{l} delays. The corresponding unfolded path starting at the the node *A*_{i}, 0 ≤ *i* ≤ *J* − 1, in the *J*-unfolded DFG ...

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