Accepting Hybrid Networks of Evolutionary Processors with Special Topologies and Small Communication

TL;DR

This paper introduces restricted topologies for hybrid networks of evolutionary processors, demonstrating their computational power and efficiency in accepting recursively enumerable languages with limited communication channels.

Contribution

It proposes three practical network topologies—star, ring, and grid—for hybrid networks of evolutionary processors and analyzes their computational capabilities.

Findings

Ring-AHNEPs can simulate 2-tag systems, proving universality.

Star and grid AHNEPs can accept all recursively enumerable languages.

Networks can operate with at most 13 communication channels.

Abstract

Starting from the fact that complete Accepting Hybrid Networks of Evolutionary Processors allow much communication between the nodes and are far from network structures used in practice, we propose in this paper three network topologies that restrict the communication: star networks, ring networks, and grid networks. We show that ring-AHNEPs can simulate 2-tag systems, thus we deduce the existence of a universal ring-AHNEP. For star networks or grid networks, we show a more general result; that is, each recursively enumerable language can be accepted efficiently by a star- or grid-AHNEP. We also present bounds for the size of these star and grid networks. As a consequence we get that each recursively enumerable can be accepted by networks with at most 13 communication channels and by networks where each node communicates with at most three other nodes.