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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peer-reviewed Journal Articles, etc >
Counterexamples to the long-standing conjecture on the complexity of BDD binary operations
| Title: | Counterexamples to the long-standing conjecture on the complexity of BDD binary operations |
| Authors: | Yoshinaka, Ryo Browse this author | | Kawahara, Jun Browse this author | | Denzumi, Shuhei Browse this author | | Arimura, Hiroki Browse this author →KAKEN DB | | Minato, Shin-ichi Browse this author →KAKEN DB |
| Keywords: | Analysis of algorithms | | Binary decision diagram | | Data structures |
| Issue Date: | 31-Aug-2012 |
| Publisher: | Elsevier B.V. |
| Journal Title: | Information Processing Letters |
| Volume: | 112 |
| Issue: | 16 |
| Start Page: | 636 |
| End Page: | 640 |
| Publisher DOI: | 10.1016/j.ipl.2012.05.007 |
| Abstract: | In this article, we disprove the long-standing conjecture, proposed by R.E. Bryant in 1986, that his binary decision diagram (BDD) algorithm computes any binary operation on two Boolean functions in linear time in the input-output sizes. We present Boolean functions for which the time required by Bryant's algorithm is a quadratic of the input-output sizes for all nontrivial binary operations, such as ⋀, ⋁, and ⊕. For the operations ⋀ and ⋁, we show an even stronger counterexample where the output BDD size is constant, but the computation time is still a quadratic of the input BDD size. In addition, we present experimental results to support our theoretical observations. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/50105 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 湊 真一
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