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ECCC
2007

Parameterized Proof Complexity: a Complexity Gap for Parameterized Tree-like Resolution

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Parameterized Proof Complexity: a Complexity Gap for Parameterized Tree-like Resolution
We propose a proof-theoretic approach for gaining evidence that certain parameterized problems are not fixed-parameter tractable. We consider proofs that witness that a given propositional formula cannot be satisfied by a truth assignment that sets at most k variables to true, considering k as the parameter. One could separate the parameterized complexity classes FPT and W[2] by showing that there is no proof system (for CNF formulas) that admits proofs of size f(k)nO(1) where f is a computable function and n represents the size of the propositional formula. We provide a first step and show that tree-like resolution does not admit such proofs. We obtain this result as a corollary to a meta-theorem, the main result of this paper. The meta-theorem extends Riis’ Complexity Gap Theorem for tree-like resolution. Riis’ result establishes a dichotomy between polynomial and exponential size tree-like resolution proofs for propositional formulas that uniformly encode a first-order prin...
Stefan S. Dantchev, Barnaby Martin, Stefan Szeider
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where ECCC
Authors Stefan S. Dantchev, Barnaby Martin, Stefan Szeider
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