1 System theoretic approach of information processing in nested cellular automata Jerzy Szynka
2025-04-27
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System theoretic approach of information processing in nested cellular automata
Jerzy Szynka
Retired researcher at the Łukasiewicz Research Network Institute of Microelectronics and Photonics
(formerly the Institute of Electron Technology), Warsaw, Poland
Abstract
The subject of this paper is the evolution of the concept of information processing in regular
structures based on multi-level processing in nested cellular automata. The essence of the proposed
model is a discrete space-time containing nested orthogonal space-times at its points.
The factorization of the function describing the global behavior of a system is the key element of the
mathematical description. Factorization describes the relations of physical connections, signal
propagation times and signal processing to global behavior.
In the model appear expressions similar to expressions used in the Special Relativity Theory.
Keywords: nested cellular automata, discrete space-time physics, relativity, neural networks,
neuromorphic computing.
1. Introduction
The idea of information processing in regular structures was first put forward by John von Neumann,
Stanislaw Ulam, and Konrad Zuse. This idea was later developed in various aspects under the
following names: cellular automata, computing space, tessellation structure, systolic array, threshold
network [1],[2],[3]. Today, this concept and its implementation in silicon is being realized under the
name of neuromorphic computing e.g. Intel Neuromorphic Research Community.
Research into information processing (signal and image recognition, data mining, deep learning) in
regular structures was inspired by neural networks and is being currently applied to artificial
intelligence solutions.
A popular cellular automaton model is a regular network of interconnected cells performing identical
logical functions.
2
Fig.1 2-dimensional cellular automaton.
This paper starts with a theoretical description of a cellular automaton, and then extends this
description to discuss multi-nested cellular automata model whose characteristic features are nested
orthogonal space-times. Algebraic description for such model will be presented.
2. Mathematical description of nested cellular automaton
The starting point is a cellular automaton. For the clarity of description and illustration, the
description of the cellular automaton is presented for one-dimensional space
R
.
Fig.2 Propagation and processing of signals in the cellular automaton.
R
is discrete space,
T
is discrete time
,
x
is the input,
s
the state and
y
the output of a cell.
Globally, the processing of signals in discrete space-time
R x T
is described by the function
A
: 𝑆𝑅𝑥𝑇 x 𝑋𝑅𝑥𝑇 → 𝑆𝑅𝑥𝑇 x 𝑌𝑅𝑥𝑇, where 𝑆𝑅𝑥𝑇is the set of mappings of space-time
R x T
into a set of
摘要：
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1SystemtheoreticapproachofinformationprocessinginnestedcellularautomataJerzySzynkaRetiredresearcherattheŁukasiewiczResearchNetworkInstituteofMicroelectronicsandPhotonics(formerlytheInstituteofElectronTechnology),Warsaw,PolandAbstractThesubjectofthispaperistheevolutionoftheconceptofinformationprocess...
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价格：10玖币
属性：10 页
大小：487.95KB
格式：PDF
时间：2025-04-27
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