Universality in two dimensions

3 years 13 days ago
Universality in two dimensions
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 behavior. This two-dimensional rendering allows, furthermore, for a most perspicacious rendering of Turing’s universal machine.
Nachum Dershowitz, Gilles Dowek
Added 07 Apr 2016
Updated 07 Apr 2016
Type Journal
Year 2016
Authors Nachum Dershowitz, Gilles Dowek
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