Fragment of flow graph

Fragment of flow graph --- фрагмент уграфа.

A subgraph of a control flow graph [math]\displaystyle{ G }[/math] is called a fragment.

A fragment [math]\displaystyle{ A }[/math] is a subfragment of [math]\displaystyle{ B }[/math], if [math]\displaystyle{ A\subseteq B }[/math]; it is a proper subfragment if [math]\displaystyle{ A\neq B }[/math].

A node [math]\displaystyle{ p }[/math] of a fragment [math]\displaystyle{ A }[/math] is called initial (respectively, output or exit) if either [math]\displaystyle{ p }[/math] is the initial node of [math]\displaystyle{ G }[/math] (respectively, [math]\displaystyle{ p }[/math] is the terminal node of [math]\displaystyle{ G }[/math]) or an arc of [math]\displaystyle{ G }[/math] not belonging to [math]\displaystyle{ A }[/math] enters [math]\displaystyle{ p }[/math] ( respectively, leaves [math]\displaystyle{ P }[/math]).

A node [math]\displaystyle{ p }[/math] of a fragment [math]\displaystyle{ A }[/math] is called its entry if there is a part from the initial node of [math]\displaystyle{ G }[/math] to [math]\displaystyle{ p }[/math] that includes no arcs of the fragment [math]\displaystyle{ A }[/math]. [math]\displaystyle{ p }[/math] is called a terminal node of a fragment [math]\displaystyle{ A }[/math] if [math]\displaystyle{ p }[/math] does not belong to [math]\displaystyle{ A }[/math] and is a successor of a node of [math]\displaystyle{ A }[/math].

A node [math]\displaystyle{ p }[/math] of a fragment [math]\displaystyle{ A }[/math] other than the initial and terminal nodes of [math]\displaystyle{ G }[/math] is called a boundary of [math]\displaystyle{ A }[/math] if [math]\displaystyle{ p }[/math] is the initial or output node of [math]\displaystyle{ A }[/math].

Let [math]\displaystyle{ p }[/math] be a boundary node of a fragment [math]\displaystyle{ A }[/math]. It is called starting of [math]\displaystyle{ A }[/math] if [math]\displaystyle{ A }[/math] contains no predecessors of [math]\displaystyle{ p }[/math] or all successors of [math]\displaystyle{ p }[/math]. It is called finishingof [math]\displaystyle{ A }[/math] if [math]\displaystyle{ A }[/math] contains all predecessors of [math]\displaystyle{ p }[/math] or no successors of [math]\displaystyle{ p }[/math].