A perfect solution to the parity problem with elementary cellular automaton 150 under asynchronous update
item.page.type
Artigo
Date
2019
item.page.ispartof
Information Sciences
item.page.citationsscopus
6
Authors
Ruivo E.L.P.
de Oliveira P.P.B.
de Oliveira P.P.B.
publication.page.advisor
Journal Title
Journal ISSN
Volume Title
publication.page.board
publication.page.program
Abstract
© 2019Cellular automata are locally-defined, fully discrete dynamical systems. One of the core questions in their study is whether or not they are capable of answering a global question about a configuration, by performing only local computations. Such decision problems include classical ones, such as the density classification task and the parity problem. Traditionally, all cells of a cellular automaton are updated synchronously. However, the possibility of allowing the updates to be asynchronous has raised an increasing interest. In [1], a solution to the parity problem – the determination of the parity of 1s in an arbitrary binary string – was given in terms of a synchronous one-dimensional cellular automaton with 9 neighbours. Here, we present a simpler solution to the same problem, by means of an elementary rule – binary, one-dimensional, with 3 neighbours – that works by asynchronously updating the even and odd positions of the lattice, alternately; we also precisely characterise how many times the rule must be iterated in order for the problem to be solved. Interestingly, our solution relies upon the elementary local parity rule, which apparently represents the first case of a rule able to solve a non-trivial problem both locally and globally.
Description
Keywords
item.page.scopussubject
Asynchronous update , Asynchrony , Density classification task , Elementary cellular automaton , Emergent computation , Local computation , Non trivial problems , Parity problems