Measuring logic complexity can guide pattern discovery in empirical systems

TL;DR

This paper introduces a logic-based complexity measure that effectively distinguishes function classes, extends canalisation concepts, and correlates with noise resilience, demonstrated across gene regulation, digital circuits, and propositional calculus.

Contribution

It proposes a new logic complexity measure that generalizes canalisation and links to noise resilience, validated on empirical data from multiple systems.

Findings

Logic complexity discriminates function classes effectively

It extends the concept of canalisation to a broader measure

It correlates with the resilience of functions to input noise

Abstract

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.