For most branching algorithms in Boolean logic "branching" means "variable-wise branching". We present the apparently novel technique of clause-wise branching, which is used to solve the ALLSAT problem for arbitrary Boolean functions in CNF format. Specifically, it converts a CNF into an orthogonal DNF, i.e. into an exclusive sum of products. Our method is enhanced by two ingredients: The use of a good SAT-solver and wildcards beyond the common don't-care symbol.
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