Fredkin and Toffoli Gates Implemented in Oregonator Model of Belousov-Zhabotinsky Medium

Adamatzky, Andrew

Abstract

© 2017 World Scientific Publishing Company. 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 subexcitable junctions. Local control of the BZ medium excitability is an important feature of the gates' design. An excitable thin-layer BZ medium responds to a localized perturbation with omnidirectional target or spiral excitation waves. A subexcitable BZ medium responds to an asymmetric perturbation by producing traveling localized excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform the computation. We interpret the wave-fragments as values of Boolean variables. The presence of a wave-fragment at a given site of a circuit represents the logical truth, absence of the wave-fragment - logically false. Fredkin gate consists of ten excitable channels intersecting at 11 junctions, eight of which are subexcitable. Toffoli gate consists of six excitable channels intersecting at six junctions, four of which are subexcitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.

Citation

Adamatzky, A. (2017). Fredkin and Toffoli Gates Implemented in Oregonator Model of Belousov-Zhabotinsky Medium. International Journal of Bifurcation and Chaos, 27(3), https://doi.org/10.1142/S0218127417500419

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2017
• Publication Date: Mar 1, 2017
• Deposit Date: Apr 26, 2017
• Journal: International Journal of Bifurcation and Chaos
• Print ISSN: 0218-1274
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 3
• DOI: https://doi.org/10.1142/S0218127417500419
• Keywords: Fredkin gate
• Public URL: https://uwe-repository.worktribe.com/output/890317
• Publisher URL: http://dx.doi.org/10.1142/S0218127417500419