A Picture for Complex Stochastic Boolean Systems: The Intrinsic Order Graph

  • Luis González
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3993)


Complex stochastic Boolean systems, depending on a large number n of statistically independent random Boolean variables, appear in many different scientific, technical or social areas. Each one of the 2 n binary states associated to such systems is denoted by its corresponding binary n-tuple of 0s and 1s, \(\left( u_{1},\ldots,u_{n}\right) \), and it has a certain occurrence probability \(\Pr\left\{ \left( u_{1},\ldots ,u_{n}\right) \right\} \). The ordering between the 2 n binary n-tuple probabilities, \(\Pr\left\{ \left( u_{1},\ldots,u_{n}\right) \right\} \), can be illustrated by a directed graph which “scales” them by decreasing order, the so-called intrinsic order graph. In this context, this paper provides a simple algorithm for iteratively drawing the intrinsic order graph, for any complex stochastic Boolean system and for any number n of independent random Boolean variables. The presentation is self-contained.


Directed Graph Occurrence Probability Binary String Lexicographic Order Boolean Variable 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Luis González
    • 1
  1. 1.Department of Mathematics, Research Institute IUSIANIUniversity of Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

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