Lower Bounds for resolution and cutting plane proofs and monotone computations

Journal of Symbolic Logic 62 (3):981-998 (1997)
We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits
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DOI 10.2307/2275583
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