Control Flow Graph - Domination Relationship

Domination Relationship

A block M dominates a block N if every path from the entry that reaches block N has to pass through block M. The entry block dominates all blocks.

In the reverse direction, block M postdominates block N if every path from N to the exit has to pass through block M. The exit block postdominates all blocks.

It is said that a block M immediately dominates block N if M dominates N, and there is no intervening block P such that M dominates P and P dominates N. In other words, M is the last dominator on all paths from entry to N. Each block has a unique immediate dominator.

Similarly, there is a notion of immediate postdominator : Analogous to immediate dominator.

The dominator tree is an ancillary data structure depicting the dominator relationships. There is an arc from Block M to Block N if M is an immediate dominator of N. This graph is a tree, since each block has a unique immediate dominator. This tree is rooted at the entry block. Can be calculated efficiently using Lengauer-Tarjan's algorithm.

A postdominator tree is analogous to the dominator tree. This tree is rooted at the exit block.

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