Oliver Kullmann

A relativized hierarchy of conjunctive normal forms

is introduced, recognizable and SAT decidable in polynomial

time. The corresponding hardness parameter, the first level

of inclusion in the hierarchy, is studied in detail, admitting

several characterizations, e.g., using pebble games, the space

complexity of (relativized) tree-like ...
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Stefan S. Dantchev, Barnaby Martin, Stefan Szeider

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 ... more >>>

Jacobo Toran, Florian Wörz

We show a new connection between the space measure in tree-like resolution and the reversible pebble game in graphs. Using this connection we provide several formula classes for which there is a logarithmic factor separation between the space complexity measure in tree-like and general resolution. We show that these separations ... more >>>

Susanna de Rezende

We show that tree-like resolution is not automatable in time $n^{o(\log n)}$ unless ETH is false. This implies that, under ETH, the algorithm given by Beame and Pitassi (FOCS 1996) that automates tree-like resolution in time $n^{O(\log n)}$ is optimal. We also provide a simpler proof of the result of ... more >>>