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.MFCS.2017.26
URN: urn:nbn:de:0030-drops-80767
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8076/
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Glinskih, Ludmila ; Itsykson, Dmitry

Satisfiable Tseitin Formulas Are Hard for Nondeterministic Read-Once Branching Programs

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LIPIcs-MFCS-2017-26.pdf (0.5 MB)

Abstract

We consider satisfiable Tseitin formulas TS_{G,c} based on d-regular expanders G with the absolute value of the second largest eigenvalue less than d/3. We prove that any nondeterministic read-once branching program (1-NBP) representing TS_{G,c} has size 2^{\Omega(n)}, where n is the number of vertices in G. It extends the recent result by Itsykson at el. [STACS 2017] from OBDD to 1-NBP.

On the other hand it is easy to see that TS_{G,c} can be represented as a read-2 branching program (2-BP) of size O(n), as the negation of a nondeterministic read-once branching program (1-coNBP) of size O(n) and as a CNF formula of size O(n). Thus TS_{G,c} gives the best possible separations (up to a constant in the exponent) between
1-NBP and 2-BP, 1-NBP and 1-coNBP and between 1-NBP and CNF.

BibTeX - Entry

@InProceedings{glinskih_et_al:LIPIcs:2017:8076,
  author =	{Ludmila Glinskih and Dmitry Itsykson},
  title =	{{Satisfiable Tseitin Formulas Are Hard for Nondeterministic Read-Once Branching Programs}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{26:1--26:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8076},
  URN =		{urn:nbn:de:0030-drops-80767},
  doi =		{10.4230/LIPIcs.MFCS.2017.26},
  annote =	{Keywords: Tseitin formula, read-once branching program, expander}
}

Keywords: Tseitin formula, read-once branching program, expander
Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 01.12.2017

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