Re: A question about Dominators

Robert Sherry wrote:
>
> The following paragraph is from the book Advanced Compiler Design
> Implementation by Steven S. Muchnick. I can be found on page 182.
>
> We give two approaches to computing the set of dominators of each node
> in a flowgraph. The basic idea of the first approach is that node a
> dominates node b if and only if a=b or a is the unique immediate predecessor
> of b or b has more then one immediate predecessor and for all immediate
> predecessors c of b, c is not equal to a and a dominates c.
>
> I believe that the above statement is incorrect. Please consider the
> following flowgraph.
> Nodes{ a, b, c, d, e }
> Edges{ (a,c), (a,d), (c,e), (d,e), (e,b) )
> a is the start node
>
> In this case, a dominates b. However, it violates the if and only if given
> above since b has a unique predecessor. The believe the correct statement
> would be:
>
> The basic idea of the first approach is that node a dominates
> node b if and only if a=b or a is the unique immediate predecessor of
> b or for all immediate predecessors c of b, c is not equal to a and a
> dominates c.


I think the last phrase should read "c equals a or a dominates c"
which of course simplifies to "a dominates c".


Consider
    N = { a, b, c}
    E = { (a,b), (a,c) }
    G = < N, E, a >


a is an immediate predecessor of b, but not a unique predecessor.


Remember though that this is an English description of an algorithm -
not a formal express of the algorithm, or a definition of the
dominator relation.

Return to the comp.compilers page.
Search the comp.compilers archives again.