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题名:
holographic algorithms by fibonacci gates
作者: Cai Jin-Yi ; Lu Pinyan ; Xia Mingji
会议文集: Linear Algebra and Its Applications
出版日期: 2011
关键词: Polynomial approximation
收录类别: ei
ISSN: 243795
部门归属: (1) Computer Sciences Department, University of Wisconsin - Madison, 1210 West Dayton Street, Madison, WI 53706, U.S.A.; (2) Microsoft Research Asia, #999, Zi Xing Road, Min Hang District, Shanghai, 200241, P.R. China; (3) Institute of Software, Chinese Academy of Sciences, #4 South Fourth Street, Zhong Guan Cun, Beijing 100190, P.R. China
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.
语种: 英语
内容类型: 会议论文
URI标识: http://ir.iscas.ac.cn/handle/311060/14289
Appears in Collections:软件所图书馆_会议论文

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