BIT Numerical Mathematics

, Volume 14, Issue 1, pp 1–13

Properties of boolean functions with a tree decomposition

  • G. V. Bochmann
  • W. W. Armstrong

DOI: 10.1007/BF01933112

Cite this article as:
Bochmann, G.V. & Armstrong, W.W. BIT (1974) 14: 1. doi:10.1007/BF01933112


Boolean functions that have a multiple disjoint decomposition scheme in the form of a tree are considered. Properties of such functions are given for the case that the functions are increasing, unate, and/or have no vacuous variables. The functions with a binary decomposition scheme are of special interest. The modulus of sensitivity is defined, and evaluated for some classes of functions. The modulus of sensitivity is interesting from the point of view of semantic information processing. It is found that the sensitivity for the class of functions with a given disjoint binary decomposition scheme is much smaller than for the unrestricted class of boolean functions. This indicates that these functions are potentially useful in pattern recognition of discrete data.

Copyright information

© BIT Foundations 1974

Authors and Affiliations

  • G. V. Bochmann
    • 1
  • W. W. Armstrong
    • 1
  1. 1.Department D'InformatiqueUniversite de MontrealCanada

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