Small Universal Accepting Networks of Evolutionary Processors with Filtered Connections

TL;DR

This paper improves the size bounds of universal Accepting Networks of Evolutionary Processors with Filtered Connections, showing they can be as small as 10 nodes for universality and 16 nodes for simulating nondeterministic Turing machines efficiently.

Contribution

It introduces smaller universal ANEPFCs of size 10 and 16, enhancing the efficiency and compactness of these computational models compared to previous bounds.

Findings

Universal ANEPFCs of size 10 are possible.

ANEPFCs with 16 nodes can simulate nondeterministic Turing machines efficiently.

The size bounds for universal ANEPFCs are significantly improved.

Abstract

In this paper, we present some results regarding the size complexity of Accepting Networks of Evolutionary Processors with Filtered Connections (ANEPFCs). We show that there are universal ANEPFCs of size 10, by devising a method for simulating 2-Tag Systems. This result significantly improves the known upper bound for the size of universal ANEPFCs which is 18. We also propose a new, computationally and descriptionally efficient simulation of nondeterministic Turing machines by ANEPFCs. More precisely, we describe (informally, due to space limitations) how ANEPFCs with 16 nodes can simulate in O(f(n)) time any nondeterministic Turing machine of time complexity f(n). Thus the known upper bound for the number of nodes in a network simulating an arbitrary Turing machine is decreased from 26 to 16.