Learning for Quantified Boolean Logic Satisfiability

Enrico Giunchiglia, Massimo Narizzano, and Armando Tacchella, DIST - Università di Genova

Learning, i.e., the ability to record and exploit some information which is unveiled during the search, proved to be a very effective AI technique for problem solving and, in particular, for constraint satisfaction. We introduce learning as a general purpose technique to improve the performances of decision procedures for Quantified Boolean Formulas (QBFs). Since many of the recently proposed decision procedures for QBFs solve the formula using search methods, the addition of learning to such procedures has the potential of reducing useless explorations of the search space. To show the applicability of learning for QBF satisfiability we have implemented it in QuBE, a state-of-the-art QBF solver. While the backjumping engine embedded in QuBE provides a good starting point for our task, the addition of learning required us to devise new data structures and led to the definition and implementation of new pruning strategies. We report some experimental results that witness the effectiveness of learning. Noticeably, QuBE augmented with learning is able to solve instances that were previously out if its reach. To the extent of our knowledge, this is the first time that learning is proposed, implemented and tested for QBFs satisfiability.

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