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Electronic Colloquium on Computational Complexity

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Reports tagged with reflection principles:
TR19-084 | 26th May 2019
Michal Garlik

Resolution Lower Bounds for Refutation Statements

For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in [Atserias-Müller,2019] asks whether a certain natural propositional encoding of the above statement is ... more >>>

TR20-037 | 18th March 2020
Michal Garlik

Failure of Feasible Disjunction Property for $k$-DNF Resolution and NP-hardness of Automating It

We show that for every integer $k \geq 2$, the Res($k$) propositional proof system does not have the weak feasible disjunction property. Next, we generalize a recent result of Atserias and Müller [FOCS, 2019] to Res($k$). We show that if NP is not included in P (resp. QP, SUBEXP) then ... more >>>

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