  We explore a definition of complexity based on logic functions, which are
widely used as compact descriptions of rules in diverse fields of contemporary
science. Detailed numerical analysis shows that (i) logic complexity is
effective in discriminating between classes of functions commonly employed in
modelling contexts; (ii) it extends the notion of canalisation, used in the
study of genetic regulation, to a more general and detailed measure; (iii) it
is tightly linked to the resilience of a function's output to noise affecting
its inputs. We demonstrate its utility by measuring it in empirical data on
gene regulation, digital circuitry, and propositional calculus. Logic
complexity is exceptionally low in these systems. The asymmetry between "on"
and "off" states in the data correlates with the complexity in a non-null way;
a model of random Boolean networks clarifies this trend and indicates a common
hierarchical architecture in the three systems.
