A question about Dominators

        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.


Please comment.


                                                                                                        Robert Sherry

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