Graph rewriting system (with priorities)

Graph rewriting system (with priorities) --- система переписывания графов (с приоритетами).

Let [math]\displaystyle{ C = (C_{V},C_{E}) }[/math] be a color alphabet. A rewriting rule over [math]\displaystyle{ C }[/math] consists of a connected [math]\displaystyle{ C }[/math]-labeled digraph [math]\displaystyle{ D }[/math] and a partial labeling function of [math]\displaystyle{ D }[/math] denoted by [math]\displaystyle{ \lambda }[/math]. We write [math]\displaystyle{ r = (D,\lambda) }[/math]. Note that such a rewriting rule can be more classically viewed as a pair of graphs (the left-hand-side and the right-hand-side of the rule) given by [math]\displaystyle{ (D, \lambda D) }[/math].

A graph rewriting system with priorities is defined by a triple [math]\displaystyle{ (C,P,\gt ) }[/math], where:

(1) [math]\displaystyle{ C = (C_{V}, C_{E}) }[/math] is the color alphabet,

(2) [math]\displaystyle{ P }[/math] is a finite set of rewriting rules over [math]\displaystyle{ C }[/math],

(3) [math]\displaystyle{ \gt }[/math] is a partial order on the rules of [math]\displaystyle{ P }[/math].