A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

Configurable NOR gate arrays from Belousov-Zhabotinsky micro-droplets

We investigate the Belousov–Zhabotinsky (BZ) reaction in an attempt to establish a basis for computation using chemical oscillators coupled via inhibition. The system consists of BZ droplets suspended in oil. Interdrop coupling is governed by the non-polar communicator of inhibition, Br2. We consider a linear arrangement of three droplets to be a NOR gate, where the center droplet is the output and the other two are inputs. Oxidation spikes in the inputs, which we define to be TRUE, cause a delay in the next spike of the output, which we read to be FALSE. Conversely, when the inputs do not spike (FALSE) there is no delay in the output (TRUE), thus producing the behavior of a NOR gate. We are able to reliably produce NOR gates with this behavior in microfluidic experiment