We provide a characterisation for the size of proofs in tree-like Q-Resolution by a Prover-Delayer game, which is inspired by a similar characterisation for the proof size in classical tree-like Resolution. This gives the first successful transfer of one of the lower bound techniques for classical proof systems to QBF proof systems.
We apply our technique to show the hardness of two classes of formulas for tree-like Q-Resolution. In particular, we give a proof of the hardness of the formulas of Kleine Buning et al. for tree-like Q-Resolution.