  This paper develops a parallel computational solver for computing all
satifying assignments of a Boolean system of equations defined by Boolean
functions of several variables. While there are we known solvers for
satisfiability of Boolean formulas in CNF form, these are designed primarily
for deciding satisfiability of the formula and do not address the problem of
finding all satisfying solutions. Moreover development of parallel solvers for
satisfiability problems is still an unfinished problem of Computer Science. The
solver proposed in this paper is aimed at representing all solutions of Boolean
formulas even without the CNF form with a parallel algorithm. Algorithm
proposed is applied to Boolean functions in algebraic normal form (ANF). The
algorithm is based on the idea to represent the satisfying assignments in terms
of a complete set of implicants of the Boolean functions appearing as factors
of a Boolean formula. The algorithm is effective mainly in the case when the
factors of the formula are sparse (i.e. have a small fraction of the total
number of variables). This allows small computation of a complete set of
implicants of individual factors one at a time and reduce the formula at each
step. An algorithm is also proposed for finding a complete set of orthogonal
implicants of functions in ANF. An advantages of this algorithm is that all
solutions can be represented compactly in terms of implicants. Finally due to
small and distributed computation at every step as well as computation in terms
of independent threads, the solver proposed in this paper is expected to be
useful for developing heuristics for a well scalable parallel solver for large
size problems of Boolean satisfiability over large number of processors.
