Compression with Wildcards: From CNFs to Orthogonal DNFs by Imposing the Clauses One-by-One. (4th March 2021)

• Record Type: Journal Article
• Authors: Wild, Marcel
• Is Part Of: Computer journal. Volume 65:Number 5(2022)
• Page Start: 1073
• Page End: 1087
• Publication Date: 2021-03-04
• Subjects: Allsat -- Boolean CNF -- exclusive sum of products -- compression -- wildcards -- BDD -- Donald Knuth; Computers -- Periodicals; 005.1
• DOI: 10.1093/comjnl/bxaa142
• Languages: English
• ISSNs: 0010-4620

Abstract

Abstract: We present a novel technique for converting a Boolean conjunctive normal form (CNF) into an orthogonal disjunctive normal form (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 literal by an arbitrary conjunction of positive literals.