License
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://drops.dagstuhl.de/opus/volltexte/2017/7423/
Go to the corresponding LIPIcs Volume Portal


Rossman, Benjamin

Subspace-Invariant AC^0 Formulas

pdf-format:
LIPIcs-ICALP-2017-93.pdf (0.5 MB)


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}
}

Keywords: lower bounds, size-depth tradeoff, parity, symmetry in computation
Seminar: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 06.07.2017


DROPS-Home | Fulltext Search | Imprint Published by LZI