*Nondisjoint** decomposition of monotone Boolean functions*

Jan C. Bioch

We discuss nondisjoint
decompositions of a monotone Boolean function f of

the form f =F(A,B,g(B,C)),
where A,B and C are disjoint sets of variables. If B

is the empty set then the theory of
decompositions, studied in game theory,

reliability theory etc. is well understood. However,
in the general case little or

nothing is known. We present some results
on the lattice of components g of f

for a fixed partition A,B and C, as
well as on the properties of the so-called

modular(bound) sets of f.