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Lower bounds for resolution and cutting plane proofs and monotone computations

Published online by Cambridge University Press:  12 March 2014

Pavel Pudlák
Pavel Pudlák*
Affiliation:
Mathematical Institute, Academy of Sciences of Czech Republic, Žitná 25, Praha 1, Czech Republic, E-mail: pudlak@beba.cesnet.cz
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 3 , September 1997 , pp. 981 - 998
Copyright
Copyright © Association for Symbolic Logic 1997

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