On Exponential Lower Bounds for Partially Ordered Resolution

Abstract

Is well-known that the proof size in propositional resolution is sensitive to the order of how variables are resolved on. Indeed, imposing a certain resolution order can lead to an exponential blowup compared to unrestricted resolution. In this paper we study even a weaker restriction. We require that one partition of variables is resolved on before the second partition (this is a special case of a partial order). We show that this also can lead to an exponential blowup. This helps us to understand why dynamic variable orderings in SAT solvers is so successful but also it motivates further investigation in variable orderings in SAT solvers.