# '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.

## Key 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.

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Source: https://tomesphere.com/paper/1702.06000