Fredkin and Toffoli gates implemented in Oregonator model of Belousov-Zhabotinsky medium

TL;DR

This paper demonstrates how Fredkin and Toffoli reversible logic gates can be implemented in a Belousov-Zhabotinsky medium network, using wave interactions to perform logical operations for unconventional computing.

Contribution

It introduces a novel design of reversible logic gates within a BZ medium, utilizing local excitability control and wave interactions, verified through numerical simulations.

Findings

Successful implementation of Fredkin and Toffoli gates in BZ medium

Verification through numerical integration of Oregonator equations

Potential for BZ medium in unconventional computing architectures

Abstract

A thin-layer Belousov-Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates --- Fredkin gate and Toffoli gate --- in a BZ medium network of excitable channels with sub-excitable junctions. Local control of the BZ medium excitability is an important feature of the gates' design. A excitable thin-layer BZ medium responds to a localised perturbation with omnidirectional target or spiral excitation waves. A sub-excitable BZ medium responds to an asymmetric perturbation by producing travelling localised excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform computation. We interpret the wave-fragments as values of Boolean variables. A presence of a wave-fragment at a given site of a circuit represents logical truth, absence of the wave-fragment --- logical false. Fredkin gate consists of ten excitable channels intersecting at eleven junctions eight of which are sub-excitable. Toffoli gate consists of six excitable channels intersecting at six junctions four of which are sub-excitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.