The Kleene Brouwer order generalizes the notion of a postorder traversal from finite trees to trees that are not necessarily finite.
2.
Therefore, the process of forming a matching by finding and removing pairs " vw " that are maximally far from " u " may be performed by a single postorder traversal of a breadth first search tree of the graph, rooted at " u ", in linear time . provide an alternative linear-time algorithm based on depth-first search, as well as efficient parallel algorithms for the same problem.
3.
Instruction selection is typically carried out by doing a recursive postorder traversal on the abstract syntax tree, matching particular tree configurations against templates; for example, the tree W : = ADD ( X, MUL ( Y, Z ) ) might be transformed into a linear sequence of instructions by recursively generating the sequences for t1 : = X and t2 : = MUL ( Y, Z ), and then emitting the instruction ADD W, t1, t2.
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