Addressing scheme: различия между версиями

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(Создана новая страница размером '''Addressing scheme''' --- адресующая схема. An '''addressing scheme''' for a ''transformation graph'' <math>{\mathcal G...)
 
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'''Addressing scheme''' --- адресующая схема.  
'''Addressing scheme''' — ''[[адресующая схема]].''


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


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such that the following two properties hold:
such that the following two properties hold:


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


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


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

Текущая версия от 11:31, 8 ноября 2011

Addressing schemeадресующая 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.