holographic algorithms by fibonacci gates

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	holographic algorithms by fibonacci gates
	Cai Jin-Yi; Lu Pinyan; Xia Mingji
	2011
会议录名称	Linear Algebra and Its Applications
页码	-
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
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.
关键词	Polynomial Approximation
语种	英语
内容类型	会议论文
URI标识	http://ir.iscas.ac.cn/handle/311060/14289
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Cai Jin-Yi,Lu Pinyan,Xia Mingji. holographic algorithms by fibonacci gates[C],2011:-.

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