When a reduced CFG with no cycles is reached, the expansion phase starts, and RECV sets for each interval is computed, this time from outermost to innermost.
In the forward analysis, the RECV sets contain only the elements needed to be communicated; therefore no stale data are used, and the correctness is ensured.
2) Using data-flow Equations (3), (4) and (5) in Figure 7, the RECV sets are computed in forward direction;
Step (e) Substitution phase: The symbolic set names in the resultant RECV sets are replaced with actual sets consisting of equalities and inequalities;
Step (f) Set generation phase: The Omega library is called to generate send and recv sets used by the code generator from the RECV sets.
The sixth column, on the other hand, shows the final RECV sets for the same array after the forward analysis and simplifications.