Re: iterative data flow question

"Jeremy Wright" <Jeremy.Wright@microfocus.com> writes:


> ... I have yet to come up with an example
> where a forward PO does not correspond to a reverse RPO (for graphs with
> single entry and exit).
>
> More generally, if PO() and RPO() return the set of all possible
> [reverse] post orders of a graph, and rev() returns the graph with the
> control flow edges reversed, is there a graph G such that
>
> PO(G) != RPO(rev(G))




Consider a directed graph on four nodes A, B, C, and D, with A being
the entry and D being the exit, and with edges


A->B
B->C
B->D
C->B.


A diagram may make this clearer:


A -> B -> D.
          ^
          |
          V
          C


Not only are the sets PO(G) and RPO(rev(G)) unequal, they are in fact
completely disjoint. Whether the graph is traversed forward or
reversed, C will be retreated out of before B is. Thus in any
postorder of either the graph or its reversal, C precedes B, whereas
in any reverse postoder of either the graph or its reversal, C follows
B.


  -Max Hailperin
    Professor of Computer Science
    Gustavus Adolphus College
    http://www.gustavus.edu/+max/

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