can be seen in Figure 12.10, where the first two steps in the derivation are
shown. The integers above and below the derivation string show the indices for
w and v, respectively, used to create the string.
Examine Figure 12.10 carefully to see what is happening. We want to
construct an MPC solution, so we must start with w 1 , that is, FS ⇒. This string
contains S, so to match it we have to use v 10 or v 11 . In this instance, we use v10;
this brings in w 10 , leading us to the second string in the partial derivation.
Looking at several more steps, we see that the string w 1 w i w j …is always longer
than the corresponding string v 1 v i v j …and that the first is exactly one step ahead
in the derivation. The only exception is the last step, where w 9 must be applied to
let the v-string catch up. The complete MPC solution is shown in Figure 12.11.
The construction, together with the example, indicates the lines along which the
next result is established.
Figure 12.9
Figure 12.10