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In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a program during its execution. The control-flow graph was conceived by Frances E. Allen , [ 1 ] who noted that Reese T. Prosser used boolean connectivity matrices for flow analysis before.
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Control-flow diagrams were developed in the 1950s, and are widely used in multiple engineering disciplines. They are one of the classic business process modeling methodologies, along with flow charts, drakon-charts, data flow diagrams, functional flow block diagram, Gantt charts, PERT diagrams, and IDEF. [2]
In computer science, control-flow analysis (CFA) is a static-code-analysis technique for determining the control flow of a program. The control flow is expressed as a control-flow graph (CFG). For both functional programming languages and object-oriented programming languages , the term CFA, and elaborations such as k -CFA, refer to specific ...
English: Some examples of control flow graphs (CFG): (a) the CFG of a if-then-else (b) a while loop (c) a natural loop with two exits, e.g. while with an if...break in the middle; non-structured by reducible (d) an irreducible CFG: a loop with to entry points, e.g. goto into a while loop Source code in DOT, svg generated with graphviz:
If a (connected) control-flow graph is considered a one-dimensional CW complex called , the fundamental group of will be (). The value of n + 1 {\displaystyle n+1} is the cyclomatic complexity. The fundamental group counts how many loops there are through the graph up to homotopy, aligning as expected.