NOT.7:5.1 - Turn prerequisite lookup into downstream search

A small dependency account gives the immediate inputs of four tasks:

This form answers “what does D need?” directly: B and C. The new working question is “after A changes, which tasks may need reconsideration?” The reader must repeatedly search the input column for dependents, then do so again for each newly found task.

Construct the reverse index: A → {B, C}, B → {D}, C → {D}, D → {}. Here an arrow goes from a supplied input to a task using it. Starting at A, follow arrows and retain newly reached tasks until none remains. The resulting set is {B, C, D}; D is retained once even though two paths reach it.

The repair changes the lookup arrangement and supplies a reading procedure. It does not add a new dependency. It makes the required direction directly available, but finding the immediate inputs of D is now less direct. Keep the original table as a complementary view if that operation remains frequent, using NOT.6 to maintain the connection.

Now remove C from D’s input list. Remove the arrow from C to D as well. A still reaches D through B. A reader who merely drops D from the downstream set has confused removal of one path with removal of every path. The changed case tests the reading operation, not the prettiness of the index.

This construction demonstrates the dependencies and operations preserved. It supplies no measured claim that every reader finds the index faster; the local display and reading conditions can change that comparison.