International Workshop on Graph Structures for Knowledge Representation and Reasoning

Graph Structures for Knowledge Representation and Reasoning pp 72-88 | Cite as

Combinatorial Results on Directed Hypergraphs for the SAT Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9501)

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.

Keywords

Directed Edge Vertex Cover Conjunctive Normal Form Propositional Variable Truth Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University Al. I. CuzaIasiRomania
  2. 2.LIRMMUniversity MontpellierMontpellierFrance

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