Abstract
We study the first level of a conjunctive normal form (CNF) formula hierarchy with respect to the propositional satisfiability problem (SAT). This hierarchy is defined over a base formula that we call a hypercube (formula). Such a hypercube simply consists of all 2n possible n-clauses over a given set of n Boolean variables. The first level of the hierarchy are 1-hyperjoins, meaning that arbitrary hypercubes are joined together via taking from each arbitrary many clauses for joining, i.e., set-union, such that each chosen clause occurs in at most one new clause of the 1-hyperjoin. We prove that arbitrary 1-hyperjoins can efficiently be recognized and solved w.r.t. SAT. To that end we introduce a simple closure concept on the set of the propositional variables of a formula.
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© 2007 Springer-Verlag Berlin Heidelberg
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Porschen, S. (2007). A CNF Formula Hierarchy over the Hypercube. In: Orgun, M.A., Thornton, J. (eds) AI 2007: Advances in Artificial Intelligence. AI 2007. Lecture Notes in Computer Science(), vol 4830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76928-6_25
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DOI: https://doi.org/10.1007/978-3-540-76928-6_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76926-2
Online ISBN: 978-3-540-76928-6
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