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Minimum propositional proof length is NP-hard to linearly approximate

Published online by Cambridge University Press:  12 March 2014

Michael Alekhnovich ,
Sam Buss ,
Shlomo Moran  and
Toniann Pitassi
Michael Alekhnovich
Affiliation:
Faculty of Mechanics & Mathematics, Moscow State University, Russia, E-mail: michael@mail.dnttm.ru
Sam Buss
Affiliation:
Department of Mathematics, University of California, San Diego, LA Jolla. CA 92093., USA, E-mail: sbuss@ucsd.edu
Shlomo Moran
Affiliation:
Department of Computer Science, Technion, Israel Institute of Technology, Haifa. Israel 32000, E-mail: moran@cs.technion.ac.il
Toniann Pitassi
Affiliation:
Computer Science Department, University of Arizona, Tucson, AZ 85721., USA, E-mail: toni@cs.arizona.edu
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Abstract

We prove that the problem of determining the minimum propositional proof length is NP-hard to approximate within a factor of . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution. Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by number of symbols or by number of inferences, for tree-like or dag-like proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 171 - 191
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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