Algorithmica

, Volume 80, Issue 10, pp 2725–2741 | Cite as

A Moderately Exponential Time Algorithm for k-IBDD Satisfiability

Article
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Abstract

We present a satisfiability algorithm for k-indexed binary decision diagrams (k-IBDDs). The proposed exponential space and deterministic algorithm solves the satisfiability of k-IBDDs, i.e., k-IBDD SAT, for instances with n variables and cn nodes in \(O\left( 2^{(1-\mu _k(c))n}\right) \) time, where \(\mu _k(c) = \varOmega \left( \frac{1}{(k^2 2^k\log {c})^{2^{k-1}-1}}\right) \). We also provide a polynomial space and deterministic algorithm that solves a k-IBDD SAT of polynomial size for any constant \(k \ge 2\) in \(O\left( 2^{ n - n^{ 1/2^{k-1} }}\right) \) time. In addition, the proposed algorithm is applicable to equivalence checking of two IBDDs.

Keywords

Indexed binary decision diagram Ordered binary decision diagram Satisfiability Moderately exponential time 
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Notes

Acknowledgements

This work was supported by MEXT KAKENHI JP24106003, JSPS KAKENHI JP26730007, JST, ERATO, Kawarabayashi Large Graph Project.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Atsuki Nagao
    • 1
  • Kazuhisa Seto
    • 2
  • Junichi Teruyama
    • 3
    • 4
  1. 1.The University of Electro-CommunicationsChofuJapan
  2. 2.Seikei UniversityMusashinoJapan
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.JST, ERATO, Kawarabayashi Large Graph ProjectTokyoJapan

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