  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.
