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The 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'02)
A Switching Lemma for Small Restrictions and Lower Bounds for k -DNF Resolution
Vancouver, BC, Canada
November 16-November 19
ISBN: 0-7695-1822-2
ASCII Text
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Nathan Segerlind, Sam Buss, Russell Impagliazzo, "A Switching Lemma for Small Restrictions and Lower Bounds for k -DNF Resolution," Foundations of Computer Science, Annual IEEE Symposium on, pp. 604, The 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'02), 2002.
 
 
BibTex
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@article{ 10.1109/SFCS.2002.1181984,
author = {Nathan Segerlind and Sam Buss and Russell Impagliazzo},
title = {A Switching Lemma for Small Restrictions and Lower Bounds for k -DNF Resolution},
journal ={Foundations of Computer Science, Annual IEEE Symposium on},
volume = {0},
year = {2002},
issn = {0272-5428},
pages = {604},
doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2002.1181984},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - CONF
JO - Foundations of Computer Science, Annual IEEE Symposium on
TI - A Switching Lemma for Small Restrictions and Lower Bounds for k -DNF Resolution
SN - 0272-5428
SP
EP
A1 - Nathan Segerlind,
A1 - Sam Buss,
A1 - Russell Impagliazzo,
PY - 2002
KW - null
VL - 0
JA - Foundations of Computer Science, Annual IEEE Symposium on
ER -
 

We prove a new switching lemma that works for restrictions that set only a small fraction of the variables and is applicable to DNFs with small conjunctions. We use this to prove lower bounds for the Res(k) propositional proof system, an extension of resolution which works with k -DNFs instead of clauses. We also obtain an exponential separation between depth d circuits of bottom fan-in k and depth d circuits of bottom fan-in k +1. Our results for Res(k) are:

  • 1. The 2n to n weak pigeonhole principle requires exponential size to refute in Res(k), for k \leqslant \sqrt {{{\log n} \mathord{\left/ {\vphantom {{\log n} {\log \log n}}} \right. \kern-\nulldelimiterspace} {\log \log n}}}.
  • 2. For each constant k, there exists a constant w>k so that random w -CNFs require exponential size to refute in Res(k).
  • 3. For each constant k , there are sets of clauses which have polynomial size Res(k+1) refutations, but which require exponential size Res(k) refutations.

    • Citation:
    Nathan Segerlind, Sam Buss, Russell Impagliazzo, "A Switching Lemma for Small Restrictions and Lower Bounds for k -DNF Resolution," focs, pp.604, The 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'02), 2002
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