abstract = "The two-bit multiplier is a simple electronic circuit,
small enough to be evolvable, and practically useful
for the implementation of many digital systems. In this
paper, we study the structure of the two-bit multiplier
fitness landscapes generated by circuit evolution on an
idealised model of a field-programmable gate array. The
two-bit multiplier landscapes are challenging. The
difficulty in studying these landscapes stems from the
genotype representation which allows us to evolve the
functionality and connectivity of an array of logic
cells. Here, the genotypes are simply strings defined
over two completely different alphabets. This makes the
study of the corresponding landscapes much more
involved. We outline a model for studying the two-bit
multiplier landscapes and estimate the amplitudes
derived from the Fourier transform of these landscapes.
We show that the two-bit multiplier landscapes can be
characterised in terms of subspaces, determined by the
interactions between the genotype partitions.",