Feasible Interpolation for QBF Resolution Calculi

Abstract

In sharp contrast to classical proof complexity we are currently short oflower bound techniques for QBF proof systems. In this paper we establish thefeasible interpolation technique for all resolution-based QBF systems, whethermodelling CDCL or expansion-based solving. This both provides the first generallower bound method for QBF proof systems as well as largely extends the scopeof classical feasible interpolation. We apply our technique to obtain newexponential lower bounds to all resolution-based QBF systems for a new class ofQBF formulas based on the clique problem. Finally, we show how feasibleinterpolation relates to the recently established lower bound method based onstrategy extraction