Achieving universal computations on one-dimensional cellular automata

Authors:
Jean-Baptiste Yunès
Affiliations:
Laboratoire d’Informatique et Algorithmique, Fondements et Applications, Université Paris Diderot & CNRS, Paris
Venue:
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Year:
2010

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Abstract

We show how natural universal computations can be achieved on one-dimensional cellular automata. That model of computation is obviously Turing complete but how can we effectively program any given computation is far less known. In this paper we are interested in intrinsic universality; we want a CA in which any other CA can be represented and simulated with no intermediate coding relevant to another computation model. The first step is to abstract from the space-time diagram in favor of a more essential dependency graph. Then such dependency graph can be projected on grids. This work shows that grids put forward causality in place of space-time contingencies.