mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, a single-entry single-exit (SESE) region in a given graph is an ordered edge pair. For example, with the ordered edge pair, (''a'', ''b'') of distinct control-flow edges ''a'' and ''b'' where: #''a'' dominates ''b''
#''b'' postdominates ''a''
# Every cycle containing ''a'' also contains ''b'' and vice versa. where a node ''x'' is said to dominate node ''y'' in a directed graph if every path from start to ''y'' includes ''x''. A node ''x'' is said to postdominate a node ''y'' if every path from ''y'' to end includes ''x''. So, ''a'' and ''b'' refer to the entry and exit edge, respectively. * The first condition ensures that every path from start into the region passes through the region’s entry edge, ''a''. * The second condition ensures that every path from inside the region to end passes through the region’s exit edge, ''b''. * The first two conditions are necessary but not enough to characterize SESE regions: since backedges do not alter the dominance or postdominance relationships, the first two conditions alone do not prohibit backedges entering or exiting the region. * The third condition encodes two constraints: every path from inside the region to a point 'above' ''a'' passed through ''b'', and every path from a point 'below' ''b'' to a point inside the region passes through ''a''.The program structure tree: computing control regions in linear time
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Graph theory objects {{graph-stub