Properties of boolean functions with a tree decomposition
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.
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