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Title:
a computational proof of complexity of some restricted counting problems
Author: Cai Jin-Yi ; Lu Pinyan ; Xia Mingji
Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Conference Name: 6th Annual Conference on Theory and Applications of Models of Computation, TAMC 2009
Conference Date: 43969
Issued Date: 2009
Conference Place: Changsha, China
Keyword: Algebra
Publisher: Germany
Publish Place: Germany
Indexed Type: 其他
ISSN: 3029743
ISBN: 9783642020162
Department: (1) Computer Sciences Department, University of Wisconsin, Madison, WI 53706, United States; (2) Microsoft Research Asia, Beijing, 100190, China; (3) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
Sponsorship: South Central University
English Abstract: We explore a computational approach to proving intractability of certain counting problems. More specifically we study the complexity of Holant of 3-regular graphs. These problems include concrete problems such as counting the number of vertex covers or independent sets for 3-regular graphs. The high level principle of our approach is algebraic, which provides sufficient conditions for interpolation to succeed. Another algebraic component is holographic reductions. We then analyze in detail polynomial maps on r2 induced by some combinatorial constructions. These maps define sufficiently complicated dynamics of r2 that we can only analyze them computationally. We use both numerical computation (as intuitive guidance) and symbolic computation (as proof theoretic verification) to derive that a certain collection of combinatorial constructions, in myriad combinations, fulfills the algebraic requirements of proving #P-hardness. The final result is a dichotomy theorem for a class of counting problems. © Springer-Verlag Berlin Heidelberg 2009.
Language: 英语
Content Type: 会议论文
URI: http://ir.iscas.ac.cn/handle/311060/8514
Appears in Collections:计算机科学国家重点实验室 _会议论文

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Recommended Citation:
Cai Jin-Yi,Lu Pinyan,Xia Mingji. a computational proof of complexity of some restricted counting problems[C]. 见:6th Annual Conference on Theory and Applications of Models of Computation, TAMC 2009. Changsha, China. 43969.
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