Turing Tumble is Turing-Complete
Formal Languages and Automata Theory
2021-10-19 v1 Computational Complexity
Abstract
It is shown that the toy Turing Tumble, suitably extended with an infinitely long game board and unlimited supply of pieces, is Turing-Complete. This is achieved via direct simulation of a Turing machine. Unlike previously informally presented constructions, we do not encode the finite control infinitely many times, we need only one trigger/ball-hopper pair, and we prove our construction correct. We believe this is the first natural extension of a marble-based computer that has been shown to be universal.
Keywords
Cite
@article{arxiv.2110.09343,
title = {Turing Tumble is Turing-Complete},
author = {Lenny Pitt},
journal= {arXiv preprint arXiv:2110.09343},
year = {2021}
}