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DOI: 10.4230/LIPIcs.MFCS.2017.26
URN: urn:nbn:de:0030-drops-80767
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8076/
Glinskih, Ludmila ; Itsykson, Dmitry
Satisfiable Tseitin Formulas Are Hard for Nondeterministic Read-Once Branching Programs
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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 | |
| Seminar: | 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 01.12.2017 |
