Parameterized Resolution with bounded conjunction
Stefan Dantchev, Barnaby Martin
TL;DR
This paper explores the differences between parameterized resolution proof systems Res(1) and Res(2), as well as their tree-Resolution counterparts, Res*(1) and Res*(2), highlighting their separations.
Contribution
It introduces new parameterized contradictions to demonstrate separations between these proof systems, advancing understanding of their relative strengths.
Findings
Res(1) and Res(2) are separated in the parameterized setting
Res*(1) and Res*(2) are also separated using new contradictions
The work clarifies the hierarchy of parameterized resolution systems
Abstract
We provide separations between the parameterized versions of Res(1) (Resolution) and Res(2). Using a different set of parameterized contradictions, we also separate the parameterized versions of Res*(1) (tree-Resolution) and Res*(2).
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Taxonomy
TopicsAdvanced Graph Theory Research · Constraint Satisfaction and Optimization · semigroups and automata theory