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Electronic Colloquium on Computational Complexity

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All reports by Author Jan Johannsen:

TR13-072 | 3rd May 2013
Jan Johannsen

Exponential Separations in a Hierarchy of Clause Learning Proof Systems

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

For every $k$ up to $O(\log n)$, an exponential separation ... more >>>

TR10-085 | 20th May 2010
Eli Ben-Sasson, Jan Johannsen

Lower bounds for width-restricted clause learning on small width formulas

It has been observed empirically that clause learning does not significantly improve the performance of a SAT solver when restricted
to learning clauses of small width only. This experience is supported by lower bound theorems. It is shown that lower bounds on the runtime of width-restricted clause learning follow from ... more >>>

TR01-056 | 6th August 2001
Michael Alekhnovich, Jan Johannsen, Alasdair Urquhart

An Exponential Separation between Regular and General Resolution

This paper gives two distinct proofs of an exponential separation
between regular resolution and unrestricted resolution.
The previous best known separation between these systems was

more >>>

TR98-035 | 8th May 1998
Maria Luisa Bonet, Juan Luis Esteban, Jan Johannsen

Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems

We prove an exponential lower bound for tree-like Cutting Planes
refutations of a set of clauses which has polynomial size resolution
refutations. This implies an exponential separation between tree-like
and dag-like proofs for both Cutting Planes and resolution; in both
cases only superpolynomial separations were known before.
In order to ... more >>>

TR97-032 | 11th July 1997
Jan Johannsen

Lower Bounds for Monotone Real Circuit Depth and Formula Size and Tree-like Cutting Planes

Using a notion of real communication complexity recently
introduced by J. Krajicek, we prove a lower bound on the depth of
monotone real circuits and the size of monotone real formulas for
st-connectivity. This implies a super-polynomial speed-up of dag-like
over tree-like Cutting Planes proofs.

more >>>

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