Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifting with Simple Gadgets and Applications to Circuit and Proof
  Complexity   We significantly strengthen and generalize the theorem lifting
Nullstellensatz degree to monotone span program size by Pitassi and Robere
(2018) so that it works for any gadget with high enough rank, in particular,
for useful gadgets such as equality and greater-than. We apply our generalized
theorem to solve two open problems:
  * We present the first result that demonstrates a separation in proof power
for cutting planes with unbounded versus polynomially bounded coefficients.
Specifically, we exhibit CNF formulas that can be refuted in quadratic length
and constant line space in cutting planes with unbounded coefficients, but for
which there are no refutations in subexponential length and subpolynomial line
space if coefficients are restricted to be of polynomial magnitude.
  * We give the first explicit separation between monotone Boolean formulas and
monotone real formulas. Specifically, we give an explicit family of functions
that can be computed with monotone real formulas of nearly linear size but
require monotone Boolean formulas of exponential size. Previously only a
non-explicit separation was known.
  An important technical ingredient, which may be of independent interest, is
that we show that the Nullstellensatz degree of refuting the pebbling formula
over a DAG G over any field coincides exactly with the reversible pebbling
price of G. In particular, this implies that the standard decision tree
complexity and the parity decision tree complexity of the corresponding
falsified clause search problem are equal.

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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc