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Title of Journal: Ann Oper Res

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Abbravation: Annals of Operations Research

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Springer US

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DOI

10.1007/bf02711193

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1572-9338

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Relations between threshold and Emphasis Type="It

Authors: David Kronus
Publish Date: 2010/08/24
Volume: 188, Issue: 1, Pages: 263-278
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Abstract

Every kinterval Boolean function f can be represented by at most k intervals of integers such that vector x is a truepoint of f if and only if the integer represented by x belongs to one of these k disjoint intervals Since the correspondence of Boolean vectors and integers depends on the order of bits an interval representation is also specified with respect to an order of variables of the represented function Interval representation can be useful as an efficient representation for special classes of Boolean functions which can be represented by a small number of intervals In this paper we study inclusion relations between the classes of threshold and kinterval Boolean functions We show that positive 2interval functions constitute a proper subclass of positive threshold functions and that such inclusion does not hold for any k2 We also prove that threshold functions do not constitute a subclass of kinterval functions for any k

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