ALLSAT compressed with wildcards: From CNF's to orthogonal DNF's by imposing the clauses one by one
This is an incremental improvement for Boolean function representation in computational logic, with potential applications in verification or optimization.
The paper tackles the problem of converting Boolean CNF formulas into orthogonal DNFs by imposing clauses sequentially, resulting in a method that is most efficient for few but large clauses and uses wildcards for compression.
We present a novel technique for converting a Boolean CNF into an orthogonal DNF, aka exclusive sum of products. Our method (which will be pitted against a hardwired command from Mathematica) zooms in on the models of the CNF by imposing its clauses one by one. Clausal Imposition invites parallelization, and wildcards beyond the common don't-care symbol compress the output. The method is most efficient for few but large clauses. Generalizing clauses one can in fact impose superclauses. By definition, superclauses are obtained from clauses by substituting each positive litereal by an arbitrary conjunction of positive literals.