# A complexity gap for tree resolution

@article{Riis2001ACG, title={A complexity gap for tree resolution}, author={S\oren Riis}, journal={computational complexity}, year={2001}, volume={10}, pages={179-209} }

- Published 2001 in computational complexity
DOI:10.1007/s00037-001-8194-y

This paper shows that any sequence $ \psi_ n $ of tautologies which expresses the validity of a fixed combinatorial principle either is “easy”, i.e. has polynomial size tree-resolution proofs, or is “difficult”, i.e. requires exponential size tree-resolution proofs. It is shown that the class of tautologies which are hard (for tree resolution) is identical to the class of tautologies which are based on combinatorial principles which are violated for infinite sets. Further it is shown that the… CONTINUE READING

#### From This Paper

##### Topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-10 of 36 extracted citations

## Resolution and pebbling games

View 6 Excerpts

Highly Influenced

## Resolution and the binary encoding of combinatorial principles

View 6 Excerpts

Highly Influenced

## The Riis Complexity Gap for QBF Resolution

View 12 Excerpts

Highly Influenced

## Parameterized Proof Complexity and W[1]

View 4 Excerpts

Highly Influenced

## Cutting Planes and the Parameter Cutwidth

View 5 Excerpts

Highly Influenced

## Parameterized Proof Complexity

View 9 Excerpts

Highly Influenced

## Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems

View 2 Excerpts

Highly Influenced

## Towards a unified complexity theory of total functions

View 2 Excerpts

## The Treewidth of Proofs MoritzMüller and

View 3 Excerpts

## The treewidth of proofs

View 3 Excerpts

#### References

##### Publications referenced by this paper.

Showing 1-10 of 28 references

## Independence in Bounded Arithmetic

View 15 Excerpts

Highly Influenced

## Lower Bound on Hilbert's Nullstellensatz and propositional proofs

View 5 Excerpts

Highly Influenced

## The Complexity of the Pigeonhole Principle

View 4 Excerpts

Highly Influenced

## Orders of Infinity, Cambridge Univ

View 4 Excerpts

Highly Influenced

## Making infinite structures finite in models of Second Order Bounded Arithmetic

View 3 Excerpts

Highly Influenced

## Introduction to Proof Theory

## A complexity gap for tree resolution

View 3 Excerpts

## Count( qq) versus the pigeon-hole principle

View 3 Excerpts