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 2n vertices, corresponding to the 2n binary n-tuples \(\left ({u}_{1},\ldots,{u}_{n}\right ) \in {\left \{0,1\right \}}^{n}\)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.
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Acknowledgments
This work was partially supported by the Spanish Government, “Ministerio de Economía y Competitividad”, and FEDER, through Grant contract: CGL2011-29396-C03-01.
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González, L. (2013). Duality in Complex Stochastic Boolean Systems. In: Ao, SI., Gelman, L. (eds) Electrical Engineering and Intelligent Systems. Lecture Notes in Electrical Engineering, vol 130. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2317-1_2
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DOI: https://doi.org/10.1007/978-1-4614-2317-1_2
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