On Exponential Lower Bounds for Partially Ordered Resolution

Mikolas Janota

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.


Keywords


resolution, lower bounds, resolution order, SAT

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