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We explore a definition of complexity based on logic functions, which arewidely used as compact descriptions of rules in diverse fields of contemporaryscience. Detailed numerical analysis shows that (i) logic complexity iseffective in discriminating between classes of functions commonly employed inmodelling contexts; (ii) it extends the notion of canalisation, used in thestudy of genetic regulation, to a more general and detailed measure; (iii) itis tightly linked to the resilience of a function's output to noise affectingits inputs. We demonstrate its utility by measuring it in empirical data ongene regulation, digital circuitry, and propositional calculus. Logiccomplexity 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 commonhierarchical architecture in the three systems.

Measuring logic complexity can guide pattern discovery in empirical systems