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

03/20/2020

∙

by   Michal Garlík, et al.

∙

0

∙

share

We show that for every integer k ≥ 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 for every integer k ≥ 1, Res(k) is not automatable in polynomial (resp. quasi-polynomial, subexponential) time.