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Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity
[article]

2020
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arXiv
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pre-print

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

arXiv:2001.02144v1
fatcat:urgi4cd5vvczdnsqcnqloxsj6q