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Journal Articles Journal of Logic and Computation Year : 2013

Universality in two dimensions

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Abstract

Turing, in his immortal 1936 paper, observed that '[human] computing is normally done by writing... symbols on [two- dimensional] paper', but noted that use of a second dimension 'is always avoidable' and that 'the two-dimensional character of paper is no essential of computation'. We propose to promote two-dimensional models of computation and exploit the naturalness of two-dimensional representations of data. In particular, programs for a two-dimensional Turing machine can be recorded most naturally on its own two-dimensional input-output grid in such a transparent fashion that schoolchildren would have no difficulty comprehending their behaviour. This two-dimensional rendering allows, furthermore, for a most perspicacious rendering of Turing's universal machine.
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Dates and versions

hal-00919604 , version 1 (17-12-2013)

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Nachum Dershowitz, Gilles Dowek. Universality in two dimensions. Journal of Logic and Computation, 2013, ⟨10.1093/logcom/ext022⟩. ⟨hal-00919604⟩

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