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arXiv · 1710.01654

Computing by nowhere increasing complexity

Bar Y. Peled·Vikas K. Mishra·Avishy Y. Carmi
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Abstract

A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this two-dimensional Kolmogorov complexity the underlying automaton is shown to be capable of simulating logic circuits. It is also shown to capture trianry logic described by a quandle, a non-associative algebraic structure. A similar automaton whose rule permits at times the increase of a cell's neighborhood complexity is shown to produce animated entities which can be used as information carriers akin to gliders in Conway's game of life.

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Bar Y. Peled, Vikas K. Mishra, Avishy Y. Carmi. 2017-10-04. Computing by nowhere increasing complexity. https://arxiv.org/abs/1710.01654

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