Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automating Cutting Planes is NP-Hard}   We show that Cutting Planes (CP) proofs are hard to find: Given an
unsatisfiable formula $F$,
  1) It is NP-hard to find a CP refutation of $F$ in time polynomial in the
length of the shortest such refutation; and
  2)unless Gap-Hitting-Set admits a nontrivial algorithm, one cannot find a
tree-like CP refutation of $F$ in time polynomial in the length of the shortest
such refutation.
  The first result extends the recent breakthrough of Atserias and M\"uller
(FOCS 2019) that established an analogous result for Resolution. Our proofs
rely on two new lifting theorems: (1) Dag-like lifting for gadgets with many
output bits. (2) Tree-like lifting that simulates an $r$-round protocol with
gadgets of query complexity $O(\log r)$ independent of input length.

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The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph