Addressing scheme

Addressing scheme — адресующая схема.

An addressing scheme for a transformation graph [math]\displaystyle{ {\mathcal G} = (V_{{\mathcal G}},\Lambda_{{\mathcal G}}) }[/math] is a total function

[math]\displaystyle{ \bar{a}: V_{{\mathcal G}} \rightarrow \bar{Mo}(\Lambda_{{\mathcal G}}), }[/math]

such that the following two properties hold:

(1) for some origin vertex [math]\displaystyle{ v_{0} \in V_{{\mathcal G}} }[/math] [math]\displaystyle{ v_{0}\bar{a} = \bar{Id}_{V_{{\mathcal G}}} }[/math],

(2) for all transformations [math]\displaystyle{ \lambda \in \Lambda_{{\mathcal G}} }[/math] and all vertices [math]\displaystyle{ v \in Domain(\lambda) }[/math]

[math]\displaystyle{ (\lambda)\bar{a} = (v\bar{a}) \cdot \lambda; }[/math]

the lefthand side denotes functional application, and the righthand side denotes multiplication in [math]\displaystyle{ \bar{Mo}(\Lambda_{{\mathcal G}}) }[/math].

A transformation graph is addressable if it admits an addressing scheme.