Simulations between Network Topologies in Networks of Evolutionary Processors

José Ángel Sánchez Martín,Victor Mitrana

doi:10.3390/axioms10030183

José Ángel Sánchez Martín, Victor Mitrana

Open Access

https://doi.org/10.3390/axioms10030183

Copy DOI

Journal: Axioms	Publication Date: Aug 11, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Universidad Politécnica de Madrid

Abstract

In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively. All of these simulations are time complexity preserving—namely, each computational step in the given network is simulated by a constant number of computational steps in the constructed network. These results might be used to efficiently convert a solution of a problem based on networks of evolutionary processors provided that the underlying graph of the solution is not desired.

Highlights

Networks of evolutionary processors (NEPs for short) have been extensively investigated in the last two decades since their generative variant has been introduced in [1]
In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively
All the strings that can leave a node leave the node and copies of them enter each node connected to the left node, provided that they can pass the input filter of the arriving node

Summary

Introduction

Networks of evolutionary processors (NEPs for short) have been extensively investigated in the last two decades since their generative variant has been introduced in [1]. A rather new and attractive direction of research has been to investigate the possibility of simulating directly and efficiently one variant by another without the intermediate step of an extra computational model (Turing machine, tag-system, register machine, etc.) in between, see, e.g., [5]. This work continues this line of research by proposing direct simulations between two NEPs such that the input one is an arbitrary NEP while the output one has a predefined topology that can be a complete graph, a star graph, or a grid.

Basic Definitions

Simulating Any NEP with a Complete NEP

Simulating Any NEP with a Star NEP

Simulating Any NEP with a Grid NEP

Conclusions and Further Work