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The Compressed Word Problem for Groups (SpringerBriefs in Mathematics) 🔍
Markus Lohrey (auth.) Springer-Verlag New York, SpringerBriefs in Mathematics, SpringerBriefs in mathematics, 1, 2014
英语 [en] · PDF · 3.1MB · 2014 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
The Compressed Word Problem For Groups Provides A Detailed Exposition Of Known Results On The Compressed Word Problem, Emphasizing Efficient Algorithms For The Compressed Word Problem In Various Groups. the Author presents The Necessary Background Along With The Most Recent Results On The Compressed Word Problem To Create A Cohesive Self-contained Book Accessible To Computer Scientists As Well As Mathematicians. Readers Will Quickly Reach The Frontier Of current Research Which Makes The Book Especially Appealing For Students Looking For A Currently Active Research Topic At The intersection Of Group Theory And Computer Science. The Word Problem Introduced In 1910 By Max Dehn is One Of The Most Important Decision Problems In Group Theory. For Many Groups, Highly Efficient Algorithms For The Word Problem Exist. In Recent Years, A New Technique Based On Data Compression For Providing More Efficient Algorithms For Word Problems, Has Been Developed, By Representing Long Words Over Group Generators In A Compressed Form Using A Straight-line Program. Algorithmic Techniques Used For Manipulating Compressed Words Has Shown That The Compressed Word Problem Can Be Solved In Polynomial Time For A Large Class Of Groups Such As Free Groups, Graph Groups And Nilpotent Groups. These Results Have Important Implications For Algorithmic Questions Related To Automorphism Groups. 1. Preliminaries From Theoretical Computer Science -- 2. Preliminaries From Combinatorial Group Theory -- 3. Algorithms On Compressed Words -- 4. The Compressed Word Problem -- 5. The Compressed Word Problem In Graph Products -- 6. The Compressed Word Problem In Hnn-extensions -- 7.outlook -- References -- Index. By Markus Lohrey.
备用文件名
lgrsnf/G:\!genesis\1\SPR_NEW_2014-01\bok%3A978-1-4939-0748-9.pdf
备用文件名
nexusstc/The Compressed Word Problem for Groups/96a28b914bd193ab25ac54785c89900a.pdf
备用文件名
scihub/10.1007/978-1-4939-0748-9.pdf
备用文件名
zlib/Science (General)/Markus Lohrey (auth.)/The Compressed Word Problem for Groups_2330989.pdf
备选标题
The Compressed Word Problem for Groups [recurso electrónico
备选作者
Lohrey, Markus
备用出版商
Springer London, Limited
备用出版商
Springer US
备用版本
SpringerBriefs in mathematics, New York, NY, 2014
备用版本
United States, United States of America
备用版本
Springer Nature, New York, NY, 2014
备用版本
SpringerBriefs in Mathematics, uuuu
备用版本
Apr 05, 2014
元数据中的注释
sm23329316
元数据中的注释
{"container_title":"SpringerBriefs in Mathematics","edition":"1","isbns":["1493907476","1493907484","9781493907472","9781493907489"],"issns":["2191-8198","2191-8201"],"last_page":153,"publisher":"Springer New York","series":"SpringerBriefs in mathematics"}
元数据中的注释
Source title: The Compressed Word Problem for Groups (SpringerBriefs in Mathematics)
备用描述
The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.
Erscheinungsdatum: 05.04.2014
备用描述
Front Matter....Pages i-xii
Preliminaries from Theoretical Computer Science....Pages 1-26
Preliminaries from Combinatorial Group Theory....Pages 27-41
Algorithms on Compressed Words....Pages 43-65
The Compressed Word Problem....Pages 67-85
The Compressed Word Problem in Graph Products....Pages 87-113
The Compressed Word Problem in HNN-Extensions....Pages 115-135
Outlook....Pages 137-138
Back Matter....Pages 139-153
开源日期
2014-04-13
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