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.