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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)

Abstract

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.

Keywords

Directed Graph Occurrence Probability Binary String Lexicographic Order Boolean Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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