Fluctuation-driven computing on number-conserving cellular automata

Lee Jia

Imai Katsunobu

Zhu Qing-sheng

Information Sciences

A number-conserving cellular automaton (NCCA) is a cellular automaton in which the states of cells are denoted by integers, and the sum of all of the numbers in a configuration is conserved throughout its evolution. NCCAs have been widely used to model physical systems that are ruled by conservation laws of mass or energy. lmai et al. [13] showed that the local transition function of NCCA can be effectively translated into the sum of a binary flow function over pairs of neighboring cells. In this paper, we explore the computability of NCCAs in which the pairwise number flows are performed at fully asynchronous timings. Despite the randomness that is associated with asynchronous transitions, useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations [18]. Specifically, certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space, as if they were subject to Brownian motion. Because random fluctuations promise a powerful resource for searching through a computational state space, the Brownian-like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous NCCA.

Cellular automaton

Number-conserving

Brownian motion

Asynchronous circuit

Petri net

Universal computation

Information science [ 007 ]

eng

Elsevier Science Inc

This is a preprint of an article submitted for consideration in Information Sciences (c) 2012 Elsevier Inc. ; Information Sciences are available online at ScienceDirect with the open URL of your article;

[ISSN] 0020-0255

[DOI] 10.1016/j.ins.2011.10.017

[NCID] AA00227045

[DOI] http://dx.doi.org/10.1016/j.ins.2011.10.017