Definition:Flow Chart/Represented Mapping

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.