Improving Model Counting by Leveraging Definability

Jean-Marie Lagniez, Emmanuel Lonca, Pierre Marquis

Abstract: We present a new preprocessing technique for propositional model counting. This technique leverages definability, i.e., the ability to determine that some gates are implied by the input formula Σ. Such gates can be exploited to simplify Σ without modifying its number of models. Unlike previous techniques based on gate detection and replacement, gates do not need to be made explicit in our approach. Our preprocessing technique thus consists of two phases: computing a bipartition 〈I,O〉 of the variables of Σ where the variables from O are defined in Σ in terms of I, then eliminating some variables of O in Σ. Our experiments show the computational benefits which can be achieved by taking advantage of our preprocessing technique for model counting.