ABSTRACT:
Let
{F1, ... , Fn} be a set of
n factors. Each factor Fi has a set
Vi of vi allowed values.
A choice of some factors and their values is called an interaction.
A choice of the values of all the factors (a realization) is either
"wrong" or "good".
In our cases the values of all the factors are 0 and 1. In other words,
every possible choice of values corresponds a subset of {1, ... , n}.
Let F be the family of "wrong" sets. We suppose F is monotone,
i.e. if A&subB&sub{1, ... , n} and
A&isinF then B&isinF.
In this case the smallest "wrong" interactions are the minimal members
of F. One test can ask subsets of {1, ... , n} if they are in
F or not. Our goal is to find all the minimal members of F.
In this generality it has been solved by Hansel. We examine some cases when
some restrictions are known on the family of minimal members of F.
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