Abstract
Neuronal network computation and computation by avalanche supporting networks are of interest
to the felds of physics, computer science (computation theory as well as statistical or machine
learning) and neuroscience. Here we show that computation of complex Boolean functions arises
spontaneously in threshold networks as a function of connectivity and antagonism (inhibition),
computed by logic automata (motifs) in the form of computational cascades. We explain the emergent
inverse relationship between the computational complexity of the motifs and their rank-ordering by
function probabilities due to motifs, and its relationship to symmetry in function space. We also show
that the optimal fraction of inhibition observed here supports results in computational neuroscience,
relating to optimal information processing.