A Hybrid Approach for SAT

Djamal Habet (1) , Chu Min Li (2) , Laure Brisoux Devendeville (2) , Michel Vasquez (3)

1 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
2 LaRIA - Laboratoire de Recherche en Informatique d'Amiens
3 LGI2P - Laboratoire de Génie Informatique et Ingénierie de Production

Exploiting variable dependencies has been shown very useful in local search algorithms for SAT. In this paper, we extend the use of such dependencies by hybridizing a local search algorithm, Walksat, and the DPLL procedure, Satz. At each node reached in the DPLL search tree to a fixed depth, we construct the literal implication graph. Its strongly connected components are viewed as equivalency classes. Each one is substituted by a unique representative literal to reduce the constructed graph and the input formula. Finally, the implication dependencies are closed under transitivity. The resulted implications and equivalencies are exploited by Walksat at each node of the DPLL tree. Our approach is motivated by the power of the branching rule used in Satz that may provide a valid path to a solution, and generate more implications at deep nodes. Experimental results confirm the efficiency of our approach.

Mots clés: Local search; Hybrid mode; Branching; Constraint satisfaction; Search tree; Propositional logic; Search algorithm

Domaines: Intelligence artificielle [cs.AI]

Djamal Habet, Chu Min Li, Laure Brisoux Devendeville, Michel Vasquez. A Hybrid Approach for SAT. CP 2002 : principles and practice of constraint programming, Sep 2002, Ithaca NY, United States. pp.172-184, ⟨10.1007/3-540-46135-3_12⟩. ⟨hal-00359416⟩