Abstract:
Constant structure closed
semantic systems are the systems each element of which receives
its definition through the correspondent unchangeable set of other
elements (neighbors) of the system. The definitions of the
elements change iteratively and simultaneously based on the
neighbor portraits from the previous iteration. In this paper, I
study the behavior of such model systems, starting from the zero
state, where all the system's elements are equal. The development
of constant-structure discrete time closed semantic systems may be
modelled as a discrete time coloring process on a connected graph.
Basically, I consider the iterative redefinition process on the
vertices only, assuming that the edges are plain connectors, which
do not have their own colors and do not participate in the
definition of the incident vertices. However, the iterative
coloring process for both vertices and edges may be converted to
the vertices-only coloring case by the addition of virtual
vertices corresponding to the edges assuming the colors for the
vertices and for the edges are taken from the same palette and
assigned in accordance with the same laws. I prove that the
iterative coloring (redefinition) process in the described model
will quickly degenerate into a series of pairwise isomorphic
states and discuss some directions of further research.
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