TL;DR
This paper proves that the Turing Tumble, a marble-based toy, is Turing-Complete when extended with an infinite game board and unlimited pieces, by directly simulating a Turing machine and providing a correct construction.
Contribution
It presents the first natural extension of a marble-based computer demonstrated to be universal, with a simplified and correct simulation of a Turing machine.
Findings
Turing Tumble can simulate a Turing machine with an infinite board
The construction requires only one trigger/ball-hopper pair
The proof confirms the Turing-Completeness of the extended Turing Tumble
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.
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Taxonomy
TopicsCellular Automata and Applications · Computability, Logic, AI Algorithms · semigroups and automata theory