Table of Contents
Journal of Complex Systems
Volume 2014, Article ID 428418, 9 pages
http://dx.doi.org/10.1155/2014/428418
Research Article

Complex Stochastic Boolean Systems: Comparing Bitstrings with the Same Hamming Weight

Department of Mathematics, Research Institute SIANI, University of Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, Spain

Received 31 October 2013; Accepted 11 January 2014; Published 24 March 2014

Academic Editor: Chun-Yi Su

Copyright © 2014 Luis González. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A complex stochastic Boolean system (CSBS) is a complex system depending on an arbitrarily large number of random Boolean variables. CSBSs arise in many different areas of science and engineering. A proper mathematical model for the analysis of such systems is based on the intrinsic order: a partial order relation defined on the set of all binary -tuples of 0s and 1s. The intrinsic order enables one to compare the occurrence probabilities of two given binary -tuples with no need to compute them, simply looking at the relative positions of their 0s and 1s. Regarding the analysis of CSBSs, the intrinsic order reduces the complexity of the problem from exponential ( binary -tuples) to linear ( Boolean variables). In this paper, using the intrinsic ordering, we compare the occurrence probabilities of any two binary -tuples having the same number of 1-bits (i.e., the same Hamming weight). Our results can be applied to any CSBS with mutually independent Boolean variables.