  A parallel method for computing Boolean expressions based on the properties
of finite free Boolean algebras is presented. We also show how various finite
combinatorial objects can be codded in the formalism of Boolean algebras and
counted by this procedure. Particularly, using a translation of first order
predicate formulas to propositional formulas, we give a method for constructing
and counting finite models of the first order theories. An implementation of
the method that can be run on multi-core CPUs as well as on highly parallel
GPUs is outlined.
