Elementary cellular automata as conditional Boolean formulæ
- Published
- Accepted
- Subject Areas
- Theory and Formal Methods
- Keywords
- cellular automata, computational completeness, boolean logic
- Copyright
- © 2016 Fleeman y Garcia
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2016. Elementary cellular automata as conditional Boolean formulæ. PeerJ Preprints 4:e2553v1 https://doi.org/10.7287/peerj.preprints.2553v1
Abstract
I show that any elementary cellular automata -- a class of 1-dimensional, 2-state cellular automata originally formulated by Stephen Wolfram -- can be deconstructed into a set of two Boolean operators; I also present a conjecture concerning the relationship between the set of computationally complete elementary cellular automata rules (such as rule 110, shown in section 2 to be composed of a NAND gate) and the set of elementary cellular automata rules that contain universal Boolean operators (such as rule 52, shown in section 3.1 to contain a universal Boolean operator yet has not been shown as of 2016 to be computationally complete.)
Author Comment
This is a currently unfinished, unpolished preprint submission to PeerJ Preprints. There are some minor formatting and convention errors which will be fixed in later revisions.