Holographic algorithms by Fibonacci gates
文献类型：期刊论文
| 作者 | Cai, Jin-Yi (1) ; Lu, Pinyan (2) ; Xia, Mingji (3) |
| 刊名 | Linear Algebra and Its Applications
 |
| 出版日期 | 2013 |
| 卷号 | 438期号:2页码:690-707 |
| 关键词 | Fibonacci gates Holographic algorithm Counting problems Dichotomy theorem Signature theory Matchgates |
| ISSN号 | 243795 |
| 通讯作者 | Cai, J.-Y.(jyc@cs.wisc.edu) |
| 中文摘要 | We introduce Fibonacci gates as a polynomial time computable primitive, and develop a theory of holographic algorithms based on these gates. The Fibonacci gates play the role of matchgates in Valiant's theory (Valiant (2008) [19]). They give rise to polynomial time computable counting problems on general graphs, while matchgates mainly work over planar graphs only. We develop a signature theory and characterize all realizable signatures for Fibonacci gates. For bases of arbitrary dimensions we prove a basis collapse theorem. We apply this theory to give new polynomial time algorithms for certain counting problems. We also use this framework to prove that some slight variations of these counting problems are #P-hard. Holographic algorithms with Fibonacci gates prove to be useful as a general tool for classification results of counting problems (dichotomy theorems (Cai et al. (2009) [7])). © 2011 Elsevier Inc. All rights reserved. |
| 英文摘要 | We introduce Fibonacci gates as a polynomial time computable primitive, and develop a theory of holographic algorithms based on these gates. The Fibonacci gates play the role of matchgates in Valiant's theory (Valiant (2008) [19]). They give rise to polynomial time computable counting problems on general graphs, while matchgates mainly work over planar graphs only. We develop a signature theory and characterize all realizable signatures for Fibonacci gates. For bases of arbitrary dimensions we prove a basis collapse theorem. We apply this theory to give new polynomial time algorithms for certain counting problems. We also use this framework to prove that some slight variations of these counting problems are #P-hard. Holographic algorithms with Fibonacci gates prove to be useful as a general tool for classification results of counting problems (dichotomy theorems (Cai et al. (2009) [7])). © 2011 Elsevier Inc. All rights reserved. |
| 收录类别 | SCI ; EI |
| 语种 | 英语 |
| 公开日期 | 2014-12-16 |
| 源URL | [http://ir.iscas.ac.cn/handle/311060/16952]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 推荐引用方式 GB/T 7714 | Cai, Jin-Yi ,Lu, Pinyan ,Xia, Mingji . Holographic algorithms by Fibonacci gates[J]. Linear Algebra and Its Applications,2013,438(2):690-707. |
| APA | Cai, Jin-Yi ,Lu, Pinyan ,&Xia, Mingji .(2013).Holographic algorithms by Fibonacci gates.Linear Algebra and Its Applications,438(2),690-707. |
| MLA | Cai, Jin-Yi ,et al."Holographic algorithms by Fibonacci gates".Linear Algebra and Its Applications 438.2(2013):690-707. |
入库方式： OAI收割
来源：软件研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。