On a Minimization of Variables to Represent Sparse Multi-Valued Input Decision Functions

A multiple-valued input decision function is a mapping f:P
ⁿ
→{0,1}, where P={0,1, ..., p-1}. This paper considers the learning of such a function. That is, given the TRUE-set T ⊆ P
ⁿ
and the FALSE-set F ⊆ P
ⁿ
, obtain a function f such that f(→a)=1 for any →a ∈ T, and f(→b)=0 for any →b ∈ F. We show a method to find a function such that f depends on the least number of variables. Applications of such functions include detection of poisonous mushrooms, hepatitis and breast cancer.