QCDCL with cube learning or pure literal elimination – What is best?

Abstract

Quantified conflict-driven clause learning (QCDCL) is one of the main approaches for solving quantified Boolean formulas (QBF). We formalise and investigate several versions of QCDCL that include cube learning and/or pure-literal elimination, and formally compare the resulting solving variants via proof complexity techniques. Our results show that almost all of the QCDCL variants are exponentially incomparable with respect to proof size (and hence solver running time), pointing towards different orthogonal ways how to practically implement QCDCL.