### Separations between propositional proof systems related to clause learning

Johannsen, J *(Ludwig-Maximilians-Universität München)*

Wednesday 28 March 2012, 10:00-10:30

Seminar Room 1, Newton Institute

#### Abstract

Resolution trees with lemmas (RTL) are a resolution-based propositional proof system that is related to the DLL algorithm with clause learning, with its fragments RTL(k) being related to clause learning algorithms where the width of learned clauses is bounded by k.

For every k up to O(log n), an exponential separation between the proof systems RTL(k) and RTL(k+1) is shown, indicating that a minimal increase in the width of learned clauses can lead to an exponential speed-up for clause learning algorithms.

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