Control flow graph

A control flow graph (CFG) in computer science is a representation, using graph notation, of all paths that might be traversed through a program during its execution. The control flow graph is due to Frances E. Allen, who notes that Reese T. Prosser used boolean connectivity matrices for flow analysis before.

The CFG is essential to many compiler optimizations and static analysis tools.

In a control flow graph each node in the graph represents a basic block, i.e. a straight-line piece of code without any jumps or jump targets; jump targets start a block, and jumps end a block. Directed edges are used to represent jumps in the control flow. There are, in most presentations, two specially designated blocks: the entry block, through which control enters into the flow graph, and the exit block, through which all control flow leaves.

Because of its construction procedure, in a non-trivial CFG (i.e. one with more than zero edges), every edge A→B has the property that:

The CFG can thus be obtained, at least conceptually, by starting from the program's (full) flow graph—i.e. the graph in which every node represents an individual instruction—and performing an edge contraction for every edge that falsifies the predicate above, i.e. contracting every edge whose source has a single exit and whose destination has a single entry. This contraction-based algorithm is of no practical importance, except as a visualization aid for understanding the CFG construction, because the CFG can be more efficiently constructed directly from the program by scanning it for basic blocks.

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