Definition:Flow Chart/Represented Mapping
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Definition
Let $C = \struct {V, E}$ be a flow chart.
Let $\struct {X, f_g, p_q}$ be an interpretation for $C$.
Then, the mapping represented by $C$ is a partial mapping $C_f : V_I \times X \to V_O \times X$ is defined as:
- For any $\tuple {b, x} \in V_I \times X$:
- $\tuple {b', x'} = \map {C_f} {b, x}$
- is unique such that there is a control path $\sequence {\tuple {b_j, x_j}}_j$ where:
- $b_1 = b$ and $b_N = b'$
- $x_1 = x$ and $x_N = x'$
- $b' \in V_O$
If no such control path exists, then $\map {C_f} {b, x}$ is undefined.
Also see
Sources
- 1966: Corrado Böhm and Giuseppe Jacopini: Flow Diagrams, Turing Machines And Languages With Only Two Formation Rules (Commun. ACM. Vol. 9, no. 5: pp. 366 – 371)
- 1974: S. Rao Kosaraju: Analysis of Structured Programs (J. Comput. Syst. Sci. Vol. 9, no. 3: pp. 232 – 255)