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.

• Type: Journal
• Year: 2016
• Where: LOGCOM
• Authors: Nachum Dershowitz, Gilles Dowek
• Keywords: LOGCOM 2016, Programming Languages