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254 6 Structural Pattern Recognition

Table 6.1. PDL operators and their meaning.

Operator Meaning Geometric interpretation

head(a+h)= head (h)
tail(a+b)= tail (a)

head(a) linked to head(b)
head (a-b)= head (b)
/ail (a-b)= tail (a)

tail(a) linked to tail(b)
head (axb)= head (h)
tail (axb)= tail (6)

head(a) linked to heud(b)
and
a*b toil(a) linked to mil(h)
head (a.b)= head (a)
tail (a*b)= tail (a)

head (-a)= tail (a)
-a
tail (-a)= head (a)

It can be shown that any digraph with labelled edges can be represented by a
PDL expression. Therefore, any pattern that can be represented by a digraph can
also be described by a PDL expression. As an example, let us look back to the
digraphs of Figure 6.4 and describe them with PDL strings, denoting r for the letter
"R" and e for the letter "En, respectively, using the new version of the primitives
shown in Figure 6.8:
r = (V + (-b)) + (4);
e = (vxh) + ((vxh) + h).

Note that the strings now incorporate the PDL operator symbols and the
parentheses as terminals. Note also that, in general, more than one representation is
possible. For instance, the following are also valid expressions: