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| Holographic algorithms by Fibonacci gates | |
| Cai, Jin-Yi (1); Lu, Pinyan (2); Xia, Mingji (3); Cai, J.-Y.(jyc@cs.wisc.edu) | |
| 2013 | |
| Source | Linear Algebra and Its Applications
 |
| ISSN | 243795 |
| Volume | 438Issue:2Pages:690-707 |
| English Abstract | 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.; 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. |
| Indexed Type | SCI ; EI |
| Keyword | Fibonacci Gates Holographic Algorithm Counting Problems Dichotomy Theorem Signature Theory Matchgates |
| Department | (1) Computer Sciences Department, University of Wisconsin - Madison, 1210 West Dayton Street, Madison, WI 53706, United States; (2) Microsoft Research Asia, #999 Zi Xing Road, Min Hang District, Shanghai, 200241, China; (3) Institute of Software, Chinese Academy of Sciences, #4 South Fourth Street, Zhong Guan Cun, Beijing 100190, China |
| Language | 英语 |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16952 |
| Collection | 中国科学院软件研究所 |
| Corresponding Author | Cai, J.-Y.(jyc@cs.wisc.edu) |
| Recommended Citation GB/T 7714 | Cai, Jin-Yi ,Lu, Pinyan ,Xia, Mingji ,et al. Holographic algorithms by Fibonacci gates[J]. Linear Algebra and Its Applications,2013,438(2):690-707. |
| APA | Cai, Jin-Yi ,Lu, Pinyan ,Xia, Mingji ,&Cai, J.-Y..(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. |
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