A Picture for Complex Stochastic Boolean Systems: The Intrinsic Order Graph

摘要

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 1s, (u_1, ... , u_n), and it has a certain occurrence probability Pr {(u_1, ... u_n)}. The ordering between the 2~n binary n-tuple probabilities, Pr {(u_1, ... , 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.