Duality in complex stochastic Boolean systems

Abstract

Many different complex systems depend on a large number n of mutually independent random Boolean variables. The most useful representation for these systems-usually called complex stochastic Boolean systems (CSBSs)-is the intrinsic order graph. This is a directed graph on 2 n vertices, corresponding to the 2 n binary n-tuples of 0s and 1s. In this paper, different duality properties of the intrinsic order graph are rigorously analyzed in detail. The results can be applied to many CSBSs arising from any scientific, technical, or social area. © 2013 Springer Science+Business Media, LLC.