Abstract

We define Etherealware as the concept of implementing the functionality of an algorithm by means of the clocking scheme of a cellular automaton (CA). We show, which functions can be implemented in this way, and by which CAs.

DOI: 10.5772/intechopen.80432

Keywords: cellular automaton, etherealware, asynchronous, update rule, universality, temporal order, clocking-computable

Your task: Compute a lot of different functions on n-bit inputs.

Your device: A (fixed!) cellular automaton (CA) on the (fixed!) ring or torus topology with n cells, is capable of holding one bit each.

You may not change the CA (its update rule) nor the topology. You may not enter additional information in the form of parameters (there would be no space to store them anyway)—and yet you are supposed to evaluate many different functions. The available degree of freedom is the clocking scheme of the cells, anything from synchronous to completely asynchronous is allowed.

Can you do it?

The perhaps surprising answer is: yes!

Every bijective function on the set 0; <sup>1</sup>;…; <sup>2</sup><sup>n</sup> f g � <sup>1</sup> , which acts as an even permutation is clocking-computable, as well as many non-bijective functions.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
