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.ISAAC.2017.58
URN: urn:nbn:de:0030-drops-82423
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8242/
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Nagao, Atsuki ; Seto, Kazuhisa ; Teruyama, Junichi

Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs

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LIPIcs-ISAAC-2017-58.pdf (0.5 MB)

Abstract

The satisfiability of a given branching program is to determine whether there exists a consistent path from the root to 1-sink.
In a syntactic read-k-times branching program, each variable appears at most k times in any path from the root to a sink.
We provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges that runs in time O\left(\poly(n, m^{k^2})\cdot 2^{(1-\mu(k))n}\right), where \mu(k) = \frac{1}{4^{k+1}}. Our algorithm is based on the decomposition technique shown by Borodin, Razborov and Smolensky [Computational Complexity, 1993].

BibTeX - Entry

@InProceedings{nagao_et_al:LIPIcs:2017:8242,
  author =	{Atsuki Nagao and Kazuhisa Seto and Junichi Teruyama},
  title =	{{Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{58:1--58:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8242},
  URN =		{urn:nbn:de:0030-drops-82423},
  doi =		{10.4230/LIPIcs.ISAAC.2017.58},
  annote =	{Keywords: branching program, read-k-times, satisfiability, moderately exponential time, polynomial space}
}

Keywords: branching program, read-k-times, satisfiability, moderately exponential time, polynomial space
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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