A new algorithm for complex stochastic Boolean systems

Abstract

Many different complex systems depend on a large number n of mutually independent random Boolean variables. For these systems. each one of the 2(n) possible situations is described by its corresponding binary n-tuple, (u(1), . . ., u(n)), of 0s and 1s, and it has its own occurrence probability Pr {(u(1), . . ., u(n))}. In this context, this paper provides a simple algorithm for rapidly generating all the binary n-tuples of 0s and 1s whose occurrence probabilities are always greater than or equal to (less than or equal to) the occurrence probability Pr {(u(1), . . ., u(n))} of an arbitrary fixed binary n-tuple (u(1), . . ., u(n)) is an element of {0, 1}(n). The results can be applied to many stochastic Boolean phenomena related to any scientific, technical or social area. All required previous results are described in detail, so that the presentation is self-contained.