Boolean functions with engineering applications and computer programs
Boolean functions with engineering applications and computer programs
A New Method for Ordering Binary States Probabilities in Reliability and Risk Analysis
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Fault Tree Analysis - A Bibliography
Fault Tree Analysis - A Bibliography
n-tuples of 0s and 1s: necessary and sufficient conditions for intrinsic order
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Splitting the Unity, Bisecting a Graph: Applications to Stochastic Boolean Systems
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
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Many different complex systems depend on a large number n of mutually independent random Boolean variables. For these systems, each one of the 2n possible situations is described by its corresponding binary n-tuple, (u1,...,un) , of 0s and 1s, and it has its own occurrence probability Pr{(u1,...,un)}. 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{(u1,...,un)} of an arbitrary fixed binary n-tuple (u1,...,un)∈{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.