| 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
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| Content Type: | 会议论文
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| URI: | http://ir.iscas.ac.cn/handle/311060/8514
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| Appears in Collections: | 计算机科学国家重点实验室 _会议论文
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| a computational proof of complexity of some restricted counting problems.pdf（2593KB） | -- | -- | 限制开放 | -- | 联系获取全文 |
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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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