License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.93
URN: urn:nbn:de:0030-drops-74235
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7423/
Rossman, Benjamin
Subspace-Invariant AC^0 Formulas
Abstract
The n-variable PARITY function is computable (by a well-known recursive construction) by AC^0 formulas of depth d+1 and leaf size n2^{dn^{1/d}}. These formulas are seen to possess a certain symmetry: they are syntactically invariant under the subspace P of even-weight elements in {0,1}^n, which acts (as a group) on formulas by toggling negations on input literals. In this paper, we prove a 2^{d(n^{1/d}-1)} lower bound on the size of syntactically P-invariant depth d+1 formulas for PARITY. Quantitatively, this beats the best 2^{Omega(d(n^{1/d}-1))} lower bound in the non-invariant setting.
BibTeX - Entry
@InProceedings{rossman:LIPIcs:2017:7423,
author = {Benjamin Rossman},
title = {{Subspace-Invariant AC^0 Formulas}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {93:1--93:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-041-5},
ISSN = {1868-8969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7423},
URN = {urn:nbn:de:0030-drops-74235},
doi = {10.4230/LIPIcs.ICALP.2017.93},
annote = {Keywords: lower bounds, size-depth tradeoff, parity, symmetry in computation}
}
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Keywords: |
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lower bounds, size-depth tradeoff, parity, symmetry in computation |
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Collection: |
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44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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07.07.2017 |
