A picture for complex stochastic Boolean systems: the intrinsic order graph

Abstract

Complex stochastic Boolean systems, depending on a large number n of statistically independent random Boolean variables, appear in many different scientific, technical or social areas. Each one of the 2 n binary states associated to such systems is denoted by its corresponding binary n-tuple of Os and Is, (u(1),...,u(n)), and it has a certain occurrence probability Pr{(u(1),...,u(n))}. The ordering between the 2" binary ntuple probabilities, Pr{(u(n),...,u(n))}, can be illustrated by a directed graph which "scales" them by decreasing order, the so-called intrinsic order graph. In this context, this paper provides a simple algorithm for iteratively drawing the intrinsic order graph, for any complex stochastic Boolean system and for any number n of independent random Boolean variables. The presentation is self-contained.