Computing the minimum DNF representation of Boolean functions defined by intervals

Authors:
Baruch Schieber;Daniel Geist;Ayal Zaks
Affiliations:
IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA;IBM Haifa Research Labs, University Campus, Carmel Mountains, Haifa, 31905, Israel;IBM Haifa Research Labs, University Campus, Carmel Mountains, Haifa, 31905, Israel
Venue:
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Year:
2005

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Abstract

For any two n-bit numbers a={0,1} to be the function for which f"["a","b"](x)=1 if and only if x is the binary representation of a number in the interval [a,b]. We consider the disjunctive normal form representation of such functions, and show how to compute such a representation with a minimum number of disjuncts in linear time. We also show how to compute a minimum ''disjoint'' representation; i.e., a representation in which the domains of the disjuncts are mutually disjoint. The minimum disjunctive normal form can be applied to devise efficient constraint satisfaction systems for automatic generation of test patterns.