Failure of Feasible Disjunction Property for $k$-DNF Resolution and NP-hardness of Automating It
Abstract
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 for every integer $k \geq 1$, Res($k$) is not automatable in polynomial (resp. quasi-polynomial, subexponential) time.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2020
- DOI:
- 10.48550/arXiv.2003.10230
- arXiv:
- arXiv:2003.10230
- Bibcode:
- 2020arXiv200310230G
- Keywords:
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- Computer Science - Computational Complexity;
- Mathematics - Logic;
- 03F20
- E-Print:
- arXiv admin note: text overlap with arXiv:1905.12372