Turing Tumble is Turing-Complete

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 infin...

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Bibliographic Details
Published in:Theoretical computer science Vol. 948; p. 113734
Main Author: Pitt, Lenny
Format: Journal Article
Language:English
Published: Elsevier B.V 28.02.2023
Subjects:
Computability
Marble-based computation
Models of computation
Turing tumble
Turing-complete
Models of computation
Marble-based computation
Turing-complete
Turing tumble
Computability
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2023.113734