'Viral' Turing Machines, Computation from Noise and Combinatorial Hierarchies

TL;DR

This paper explores a novel stochastic extension of Turing Machines using cellular automata with exponential waiting times, and introduces an inductive combinatorial hierarchy for analyzing such systems.

Contribution

It presents a new stochastic model of Turing computation via asynchronous cellular automata and develops a combinatorial hierarchy for analytical derivations.

Findings

Extended Turing Machine to a stochastic cellular automaton model

Introduced an inductive combinatorial hierarchy for analysis

Provided a framework for recursive relation derivation

Abstract

The interactive computation paradigm is reviewed and a particular example is extended to form the stochastic analog of a computational process via a transcription of a minimal Turing Machine into an equivalent asynchronous Cellular Automaton with an exponential waiting times distribution of effective transitions. Furthermore, a special toolbox for analytic derivation of recursive relations of important statistical and other quantities is introduced in the form of an Inductive Combinatorial Hierarchy.