Abstract
Directed hypergraphs have already been shown to unveil several combinatorial inspired results for the SAT problem. In this paper we approach the SAT problem by searching a transversal of the directed hypergraphs associated to its instance. We introduce some particular clause orderings and study their influence on the backtrack process, exhibiting a new subclass of CNF for which SAT is polynomial. Based on unit resolution and a novel dichotomous search, a new DPLL-like algorithm and a renaming-based combinatorial approach are proposed. We then investigate the study of weak transversals in this setting and reveal a new degree of a CNF formula unsatisfiability and a structural result about unsatisfiable formulae.
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Croitoru, C., Croitoru, M. (2015). Combinatorial Results on Directed Hypergraphs for the SAT Problem. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2015. Lecture Notes in Computer Science(), vol 9501. Springer, Cham. https://doi.org/10.1007/978-3-319-28702-7_5
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DOI: https://doi.org/10.1007/978-3-319-28702-7_5
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