English

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}
}
R2 v1 2026-06-24T06:58:41.498Z