Reference: Zeng, H.; McIlraith, S. Experimental Results on the Satisfiable Core in Random 3SAT. Ninth International Symposium on Artificial Intelligence and Mathematics, January 4-6, 2006, Fort Lauderdale, Florida 2006.
Abstract: Given a satisfiable k-CNF SAT instance, a satisfiable core is a minimal subset of the k-CNF clauses that preserves all and only the satisfying assignments of the original instance. In this paper, we extend the previous results on satisfiable core, especially on the strong correlation between the hardness of SAT instances and the size of their satisfiable cores. We introduce a measure called the weighted clause-to-variable ratio, which substantially improves on the classic clause-to-variable ratio in explaining the phase transition. We also examine interesting transitions in satisfiable core size of random instances and show that satisfiable core is a powerful concept for studying the constrainedness of instances.
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