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://drops.dagstuhl.de/opus/volltexte/2017/8242/
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### Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs

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### 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},