Symmetry Breaking in Quantified Boolean Formulae

Gilles Audemard, Saïd Jabbour, Lakhdar Saïs

Many reasoning task and combinatorial problems exhibit symmetries. Exploiting such symmetries has been proved to be very important in reducing search efforts. Breaking symmetries using additional constraints is currently one of the most used approaches. Extending such symmetry breaking techniques to quantified boolean formulae (QBF) is a very challenging task. In this paper, an approach to break symmetries in quantified boolean formulae is proposed. It makes an original use of universally quantified auxiliary variables to generate new symmetry breaking predicates and a new ordering of the QBF prefix is then computed leading to a new equivalent QBF formula with respect to validity. Experimental evaluation of the state-of-the-art QBF solver semprop shows significant improvements (up to several orders of magnitude) on many QBFs instances.