Understanding the Relative Strength of QBF CDCL Solvers and QBF Resolution

QBF solvers implementing the QCDCL paradigm are powerful algorithms that successfully tackle many computationally complex applications. However, our theoretical understanding of strength and limitations these is very limited. In this paper we suggest to formally model as proof systems. We define different policies can be used for decision heuristics unit propagation give rise a number sound complete systems (and hence new algorithms). With respect standard in practical solving, show corresponding system incomparable (via exponential separations) Q-resolution, classical resolution literature. This stark contrast propositional setting where CDCL known p-equivalent. raises question what formulas hard QCDCL, since Q-resolution lower bounds do not necessarily apply here. answer prove several including large class random QBFs. also introduce strengthening heuristic which does decide variables order prefix, but still allows learn asserting clauses. with policy, exponentially faster on some formulas. further exhibit p-equivalent Q-resolution. comparison version adapts both policies.