Exponential Separations in a Hierarchy of Clause Learning Proof Systems

  • Jan Johannsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7962)


Resolution trees with lemmas (RTL) are a resolution-based propositional proof system that is related to the DPLL algorithm with clause learning. Its fragments \(\ensuremath{\ensuremath{\mathrm{RTL}} ({k})}\) are related to clause learning algorithms where the width of learned clauses is bounded by k.

For every k up to O(logn), an exponential separation between the proof systems \(\ensuremath{\ensuremath{\mathrm{RTL}} ({k})}\) and \(\ensuremath{\ensuremath{\mathrm{RTL}} ({k+1})}\) is shown.


Proof System Conjunctive Normal Form Satisfying Assignment Partial Assignment Resolution Tree 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jan Johannsen
    • 1
  1. 1.Institut für InformatikLudwig-Maximilians-Universität MünchenGermany

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