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Complexities of graph-based representations for elementary functions
http://hdl.handle.net/10228/2475
http://hdl.handle.net/10228/2475b557bd01-294d-47a5-afe6-d4dbb1042e89
| 名前 / ファイル | ライセンス | アクション |
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Comprexities.pdf (2.3 MB)
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| アイテムタイプ | 学術雑誌論文 = Journal Article(1) | |||||
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| 公開日 | 2009-09-09 | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | journal article | |||||
| タイトル | ||||||
| タイトル | Complexities of graph-based representations for elementary functions | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 著者 |
Nagayama, Shinobu
× Nagayama, Shinobu× 笹尾, 勤 |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | This paper analyzes complexities of decision diagrams for elementary functions such as polynomial, trigonometric, logarithmic, square root, and reciprocal functions. These real functions are converted into integer-valued functions by using fixed-point representation. This paper presents the numbers of nodes in decision diagrams representing the integer-valued functions. First, complexities of decision diagrams for polynomial functions are analyzed, since elementary functions can be approximated by polynomial functions. A theoretical analysis shows that binary moment diagrams (BMDs) have low complexity for polynomial functions. Second, this paper analyzes complexity of edge-valued binary decision diagrams (EVBDDs) for monotone functions, since many common elementary functions are monotone. It introduces a new class of integer functions, Mp-monotone increasing function, and derives an upper bound on the number of nodes in an EVBDD for the Mp-monotone increasing function. A theoretical analysis shows that EVBDDs have low complexity for Mp-monotone increasing functions. This paper also presents the exact number of nodes in the smallest EVBDD for the n-bit multiplier function, and a variable order for the smallest EVBDD. | |||||
| 書誌情報 |
IEEE Transactions on Computers 巻 58, 号 1, p. 106-119, 発行日 2009-01 |
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| 出版社 | ||||||
| 出版者 | IEEE | |||||
| DOI | ||||||
| 関連タイプ | isIdenticalTo | |||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | https://doi.org/10.1109/TC.2008.134 | |||||
| ISSN | ||||||
| 収録物識別子タイプ | PISSN | |||||
| 収録物識別子 | 0018-9340 | |||||
| 著作権関連情報 | ||||||
| 権利情報 | Copyright (c) 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Decision diagrams | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | MTBDDs | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | EVBDDs | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | BMDs | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | elementary functions | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | kth-degree polynomial functions | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Mp-monotone increasing functions | |||||
| 出版タイプ | ||||||
| 出版タイプ | VoR | |||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
| 査読の有無 | ||||||
| 値 | yes | |||||
| 業績ID | ||||||
| 値 | D1F6BB7706A9DFAD4925762B001D239F | |||||
