Abstract
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.
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Johannsen, J. (2013). Exponential Separations in a Hierarchy of Clause Learning Proof Systems. In: Järvisalo, M., Van Gelder, A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39071-5_5
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