Propositional satisfiability: techniques, algorithms and applications
AI Communications
SAT graph-based representation: A new perspective
Journal of Algorithms
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Backdoor sets of quantified boolean formulas
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
From horn strong backdoor sets to ordered strong backdoor sets
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
Solving #SAT using vertex covers
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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Recent advances in propositional satisfiability (SAT) include studying the hidden structure of unsatisfiable formulas, i.e., explaining why a given formula is unsatisfiable. Although theoretical work o n the topic has been developed in the past, only recently two empirical successful approaches have been proposed: extracting unsatisfiable cores and identifying strong backdoors. An unsatisfiable core is a subset of clauses that defines a sub-formula that is also unsatisfiable, whereas a strong backdoor defines a subset of variables which assigned with all values allow concluding that the formula is unsatisfiable. The contribution of this paper is two-fold. First, we study the relation between the search complexity of unsatisfiable random 3-SAT formulas and the sizes of unsatisfiable cores and strong backdoors. For this purpose, we use an existing algorithm which uses an approximated approach for calculating these values. Second, we introduce a new algorithm that optimally reduces the size of unsatisfiable cores and strong backdoors, thus giving more accurate results. Experimental results indicate that the search complexity of unsatisfiable random 3-SAT formulas is related with the size of unsatisfiable cores and strong backdoors.