Multiway Turing Machines

TL;DR

This paper explores the behavior and properties of multiway Turing machines, revealing their potential for universality and their relevance to concurrent computing and quantum mechanics.

Contribution

It introduces a detailed study of multiway Turing machines with simple rules, highlighting their complex behaviors and potential universality, and connecting them to broader computational and physical theories.

Findings

Simple multiway Turing machines can generate complex multiway graphs.

Machines with minimal states and colors may be universal.

Multiway Turing machines relate to issues in concurrent computing and quantum observer models.

Abstract

Multiway Turing machines (also known as nondeterministic Turing machines or NDTMs) with explicit, simple rules are studied. Even very simple rules are found to generate complex behavior, characterized by complex multiway graphs, that can be visualized in multispace that combines "tape" and branchial space. The threshold for complex behavior appears to be machines with just s = 1 head states, k = 2 tape colors and p = 3 possible cases, and such machines may potentially be universal. Other characteristics of multiway Turing machines are also studied, including causal invariance, cyclic tapes and generalized busy beaver problems. Multiway Turing machines provide minimal examples of a variety of issues encountered in both concurrent computing and the theory of observers in quantum mechanics, especially in our recent models of physics.