Which of the following concepts can be used to identify loops? A. Depth first…

Answer: All three concepts — Depth-first ordering, Dominators, and Reducible graphs — can be used to identify loops.

Key ideas:

• Depth-first ordering: A DFS of the control-flow graph classifies edges and exposes back edges (edges to ancestors). Each back edge signals a loop and is used to form the natural loop around the loop header.

• Dominators: Dominator analysis identifies nodes that must be passed to reach others; a back edge from a node to one of its dominators indicates a natural loop with that dominator as the unique loop header, and the dominator tree helps determine loop nesting.

• Reducible graphs: If a control-flow graph is reducible, its loops are guaranteed to be natural (single-entry), which makes standard loop-detection techniques (based on back edges and dominators) correct and simpler to apply.

Note: Strongly connected components also detect cycles in general graphs, but dominator and back-edge based methods specifically identify natural single-entry loops; reducibility is the structural property that guarantees this form.